Activities for musically inclined two-year old?

Our daughter (just about 4 years old) is very similar in musical interest/ability to what you described. She's been taking group music class with Jon at Totland and loves it. 

http://www.jsom.com/jon-s-school-of-music-1

They learn about different notes and scales, do vocal exercises, and get exposure to all instruments - drum set, electric guitar and bass, violin, trumpet, cello, piano, other percussion instruments, etc.

From what I've read, she's still a little too young to be able to really form chords on a guitar. They say the best instrument for kids this age is the drums - she's always banging on a few hand drums that we have in the house and has a ukulele that she plays - her strumming and rhythm have really improved on that. Although she can't get form chords, she has started moving her fingers around and recognizes the different sounds it makes.

"Music together" classes are a great start for a two year old. As a professional musician, I recommend starting him on piano lessons around age 5. Being able to play the piano will be of help to him in the future, no matter what area of music or instrument he eventually falls in love with. When my own children were young, I asked a number of piano professors what their recommendation was, and was told that developmentally it makes sense to start formal lessons when the child is learning to read.
 

Hi there, you got the similar situation as we do, my oldest is almost 5 years old and the youngest is only 14 months. We took both boys to Jon's School of Music, they LOVE it!!! Jon is a very professional and experienced musician and teacher, he got all the skills to entertain kids while teaching and inspiring kids to learn & love music. My oldest son started taking music lesson from Jon as young as 23 months, and now almost 3 years already, and My younger is started lesson as young as 12 months old once he can sit still. And we both see music lessons have wonderful impact on them, verbal, communication, expression oneself & cognitive development. They got to experience different kind of music instruments, making songs, dancing & dramatic music play, etc., We LOVE it.
And, they also can associate with kids around their age and my kids have great friends group inside the music class too, also, so do mom support group too. :) Anyway, we do highly recommend to everyone who are looking for professional, affordable & wonderful music introduction classes.
http://www.jsom.com/jon-s-school-of-music-1

There's Jon's School of Music holds fun music classes for tots in the little clubhouse at Totland toddler park at Virginia/McGee in Berkeley. Some of the classes start as young as 1 year old.

So great that your toddler loves music. My advice would be to sing, dance, and have some inexpensive ways for him to make and enjoy his own music--a drum, shaker, inexpensive ukulele, etc... Also sign up for parent-child music classes so you can have fun with music together.  Kindermusik is a great program if there are classes near you: https://www.kindermusik.com. Many of those early music classes explore rhythm, melodies, and exposure to instruments that are easy for very young children to make sounds with.  Any class with a good teacher will be fun for him and will give him exposure to a variety of musical experiences. And they also teach you about music with activities you can do together outside of class. I think most people would agree that this is way too young for formal one-on-one instrumental training/lessons.  Even if he's truly gifted and seems driven by music, I think that for preschoolers, some kind of group music experience is often the best--with lots of exposure, but not narrowing down to one instrument or the intensity of private lessons.  Of the three kids in our family, all took early parent-child music classes and had great experiences. One kid was obsessed with music as a preschooler, and we would have predicted that he would go on to be the most musical.  In elementary school, he switched focus to other things so music was just in the background.  The other two kids enjoyed the preschool music classes, but not as much. One of those kids then begged to take trumpet lessons at age 8 and has been playing trumpet and now loves middle school band (competent, but not more than that).  The other also enjoyed middle school band but quit in high school.  For all our kids, having the exposure during the preschool years to the group music classes laid an important foundation that they could later use (or not) in more formal lessons. And if your child's interest turns out to be prodigy-level, I think that those kids let you know in some way or another that they need something different than other children, and then you figure that out! 

Try Jon’s School of Music. He’ll have a ton of fun, learn musical notes and try out many instruments.

http://www.jsom.com/

Have you heard of Cazadero Performing Arts Camp?  There are 2 sessions every August of one week each of Family Camp.  Here, campers (including little ones) are exposed to and participate in music and art activities along with great meals.  It's a wonderful experience that I got to have with my kids for over a decade while they were growing up.  It's also a very warm and loving community of folks.

We are musicians and have kids who are interested in music. We have always taken the approach of making music accessible and offering real instruments. Toys are poor quality and not in tune.  Lots of percussions, uke, recorder, harmonica, drums, marimba, piano. We always have these instruments around the house. Our kids are allowed to touch, tinker with and play a lot of instruments we own except for the most expensive ones and our family heirloom accordion. If they want to play with our gig guitar or sax, we let them but supervise them closely. This also teaches them to respect the instrument. We often dance at home. We bang tables and have percussion sessions. Music together is great for little ones. Sing together. Make up drum beats. Make instruments together. Make up silly tunes. We started piano at age 4.5. At age 7, we began a second instrument at our kids’ request. We did not push but our older one wanted to learn the violin and our younger one wanted to learn the guitar. 
 

for 2 year olds, I would get a high quality xylophone, marimba, melodica, bongo drums, harmonica, train whistle, sticks, recorder and other percussions — shakers, tambourines. Again, get something that actually sounds good. That Melissa and Doug harmonica is horribly out of tune. If you can get a piano, that is great but keyboard would be fine as well. I know some people start Suzuki lessons very early but I don’t agree that earlier is better. I personally began piano lessons at age 3.5 and my spouse didn’t start formal lessons until high school. Honestly, I think my spouse is a better instrumentalist than I am and my spouse ended up being a full time professional musician while I am just a hobbyist these days. 
 

OP here - just wanted to thank everyone for responding! It's great to get so many independent recommendations for Jon's classes at Totland - I am looking into these. And it's also very encouraging to hear from professional musicians and parents of many, somewhat older kids how interests developed and fizzled. Thanks a lot for the recommendations! 

I loved Music Together classes, held throughout the East Bay and beyond, with my two sons, starting at age 1 for the older boy and in the womb for the younger boy.  Lots of fun, much better music than most children's programs (IMO), and great "training" in general. At age 4 (or just before), I can recommend the Pacific Boychoir Academy's youngest boys program, based on the Kodaly method and every well taught. It's in Oakland off Piedmont Avenue (and near the Rockridge/Temescal neighborhoods too). I think it is great for boys to be with other boys (although there is also a new program for young girls at PBA as well!)), and this is a great program.  Singing and fun music 'instruction' at age 4 at PBA, coupled with starting piano lessons at about age 5, will allow your son to have fun and be engaged with music, use his whole body and whole brain, and get a great start no matter what type of music he may like or want to pursue as he gets older!  [My son didn't start at PBA until Age 8; he is now 15 and still going strong with them; I wish I had known about PBA even sooner!]

I also recommend Jon’s music classes at Totland park (jsom.com). My daughter started attending at around 2.5 years and all our family loves these lessons. They are both very entertaining and goofy, and educational. At first I thought of it more like a good way for my daughter to socialize and get a music exposure (she really likes singing and listening to music a lot). I didn’t expect much of the educational component. But in reality after a few lessons my daughter started repeating all the info about notes and singing in different tones at home too! So, this is not just a fun class, it’s really working in terms of building the foundation for future more structured classes for older kids. And I also love that Jon introduces kids to real instruments—guitars, drums, violin, cello etc. They play like a real rock-band during classes. And Jon himself is so good with the kids! My daughter adores him.

Here to add another endorsement for Jon's School of Music at Totland. Lots to love about his approach and, as a professor of music, I appreciate so much that his priority is play, exploration, and collaboration for kids just starting off in music. My two kids (ages 3 and 6) have learned a lot from him this last year!