Vacation for a week after Christmas

I have heard that Death Valley is nice, especially that time of year. 

If you end up going to Vegas, take your day trip to Zion National Park instead of to the Grand Canyon. Zion is absolutely gorgeous and there are a lot of beautiful hikes (e.g., Emerald Pools, the Narrows if it's safe, Angel's Landing if you want more of a challenge, and the West Rim if you really want to push it) that are accessible from the road. My experience with the Grand Canyon is that there's very little to do there if you don't actually go down into the canyon (an extremely arduous hike). Basically you park the car, look into the canyon, comment on how grand it is, and then go have an overpriced, fairly crappy lunch. I've been to the north rim (Jacob's Lake) a few times and was happy to see it but bored quickly. Maybe the south rim is more fun but I kind of doubt it. Zion, on the other hand, is gorgeous and accessible. Springdale has become a pretty trendy town and there's shopping and restaurants once you're done with the park. It's about a 3 hour drive from Vegas to Zion but so worth it. If you're really lucky it will have snowed. I've never seen a more beautiful sight than the red rock walls of Zion with snow piled on the ledges.

Those are both long drives, but between the two I would absolutely pick San Diego over Las Vegas. It's beautiful, it has a variety of activities to suit all interests and age groups, and proximity to other interesting destinations. There are neighborhoods with Airbnb options in San Diego where the older kids could walk around on their own (South Park, Little Italy, North Park etc) and you'd have easy to access to the gardens, zoo, and museums in Balboa Park plus a good location to drive to beaches in Coronado, La Jolla, and Pt Loma (my favorite tidepooling is at Pt Cabrillo if the tide charts are in your favor) plus you have the Safari Park (newish name for Wild Animal Park), Julian, Anza Borrego Desert and Tijuana as possible day trips.  If you wanted a day or two of resort experience, the greater San Diego area has plenty of options for that (Loews in Coronado, Paradise Point in Mission Bay etc). Las Vegas in December could be quite cold, which would make the pools undesirable, and I wouldn't feel as uncomfortable with kids on their own. Las Vegas has fun, but you need to pay for all of it, and it can be overwhelming for kids. That said, I know some people LOVE it. But I wouldn't choose that for a group vacation unless I knew for sure it was everyone's cup of tea.

San Diego Zoo is amazing.  Can eat Mexican food / shop in the Old Town (I think that's what they call it).  There's museums.  The beach.  There's a ship.  It would be fun, we went once during the winter several years ago.  I would check out a guidebook to see if you want to go.

We have vacationed in San Diego the week after Christmas multiple times with our 3 school age children.  Always had a great time.  Weather is usually good and lots to do.  In addition to the things you mentioned check out Balboa Park, Old Town and La Jolla Shores and LegoLand.  

I would do Palm Springs, condo or private rental home with a pool.

Those are good ideas... I'm not sure how warm are those areas in winter...I guess if you go to San Diego, you could always go to Mexico ( you would need passports) Tijuana, Rosarito, Ensenada and the wine country of Valle de Guadalupe.

Palm Springs could be also nice, restaurants, shops,bikes, pools, hikes, Joshua tree...

Have fun!