Live music for young kids?

There is lots of free live music around, https://www.musicinsf.com/best-free-live-music-san-francisco/, https://www.eventbrite.com/rally/san-francisco/free-bay-area-outdoor-su… (wow Kaiser Center roof garden concerts, that sounds awesome).

Try the Friday nights at the Oakland Museum of California.  There are always plenty of kids, and usually one music group in the ampitheater playing world music or hip hop and often a smaller jazz ensemble playing upstairs at the other entrance.  You only have to pay if you go into the galleries and there's a lot of food trucks too.  My four year old loves it!

I would definitely suggest the SF Jazz Center. While shows are "all-ages", they have special family programming too (like Family Matinee, where the performer of the week/weekend plays a special afternoon show for children/families on Sunday's, I think. The musicians play the music they would normally play during their nighttime shows, but there is also engagement with the kids in the audience): https://www.sfjazz.org/education/kids-and-family/ I have also been to Thursday-Saturday night shows and have seen several kids scattered here & there in the audience. I had SF Jazz membership for two years, but didn't renew it last year because I had a baby. When she gets older, we'll start going to shows again. 

Also, check out Ashkenaz, an all-ages world music venue in Berkeley: http://www.ashkenaz.com

All shows at Ashkenaz are all-ages (I'm not sure if kids have to pay full ticket price). You can look at the calendar and filter to see just "jazz" if that's what you're looking for, but it's a great place to explore all kinds of music (and dancing).  It can sometimes (not always) be loud, though, so consider bringing child-size ear protectors  just in case (they offer free foam earplugs for adults, in case your ears are sensitive)

http://www.ashkenaz.com/

The BPN Announcements newsletter regularly has listings for kid-friendly music performances of all kinds!  And summer street fairs, county fairs, and community festivals of all kinds typically have one or more stages with bands performing a wide variety of music - sometimes for free, and often as part of an event with lots of other activities and entertainment that should appeal to a preschooler.  The Marin County Fair has all kinds of local bands as well as famous headliner concerts, and is a great place to go for (non foggy!) July 4th fireworks; Stern Grove famously offers opera and symphonic music but there's also many other types on different dates; Oakland's Art & Soul festival features blues, gospel, and (of course) soul; both Point Richmond and Albany have an outdoor concert series; the Solano Stroll offers a different style of music or dance happening every block or two...you should be able to find something of the sort happening in the Bay Area any week between June and September!  Come fall, consider looking for the performance schedules of your local high schools' music departments; school band and choir concerts (as well as school group performances at community events) are often great options for interested younger kids -- we have a lot of amazing school jazz programs in the East Bay, and their performances are generally cheaper than professional concerts, held earlier in the evening and often in spaces that are more readily escaped without disturbing others if it turns out your child is restless.  Plus, they show young kids that they can *make* wonderful music as well as appreciate it, long before they're as old and experienced as the adult professionals.

Luckily for you, we're entering the time of year when there are a ton of free outdoor concerts around the Bay Area - perfect for small kids who might want to dip in and out of the music and have some room to explore. Check out Alameda's Concerts at the Cove (https://www.ebparks.org/activities/features/concerts_at_the_cove.htm) and Summer Beats at South Shore (http://www.alamedasouthshorecenter.com/events/), plus this big list here: http://redtri.com/san-francisco/bay-area-summer-concerts/. And of course Ashkenaz is all-ages - you can sort their calendar by genre to find jazz shows. Lastly, find out when local middle school and high school jazz bands are performing at local restaurants, Yoshi's (also all-ages), etc. - there are some really great school jazz bands around here, and you'll be supporting a local music program, too.

Stern grove open-air concert series starts in June: http://www.sterngrove.org/2018-concerts/!

The concerts at the UC Botanical Garden are great! Lots of kids!

http://botanicalgarden.berkeley.edu/summer-concerts-2018

Restaurants are good, too. I recently heard some nice harp music at Brezo in Richmond. 

https://brezorestaurant.com/

I found this: http://www.ashkenaz.com/eventcalendar?category=FAMILY

on this: https://www.510families.com/?s=live+music

I agree- avoid strictly "kids music."  (it's like kids food- blech). Don't forget earplugs.

Yerba Buena Gardens concerts: free, accessible by BART, and next to a great playground: https://ybgfestival.org/

UC Berkeley Botanical Gardens concerts: early in the evening http://botanicalgarden.berkeley.edu/summer-concerts-2018

Four Seasons Arts (http://www.fsarts.org/) has a wonderful classical music line-up.  They aim to have world-renowned, diverse musicians, and they aim to provide to a diverse audience as well.  It's a mixture of older folks (well, quite a few), but there are also children there with their adult chaperones/parents. Subscriptions to the season for the whole family are quite economical (4 concerts for a family of up to 2 adults + 2 children for $180, with adjustments for more children).  I think they host children 6 yrs. old or above, though.  Maybe in a few years...

Farmers' markets often have live music. Kensington has live music every Sunday 10-2 at their farmers market and there are always lots of kids (they provide kid-sized chairs). Although it's been years since I went to the Temescal market (by the DMV), I think they used to have live music.

Libraries offer many summer programs that fit the bill. Also, look at Berkeley’s Kidchella program, also available in Redwood City.