Santa Fe isn't the most kid-friendly city. It caters more to adults than, say, Orlando. I love SF, though, and make it there at least a couple of times a year.
Oldest house is free, but not really very interesting. Don't plan to spend more than about three minutes there, really.
Buy your tickets ahead of time for Meow Wolf, it'll save you a few minutes. Also go early. Kid will love it.
International Folk Art museum would be great for kids. The whole Museum Hill area has plenty to entertain a kid, but folk art is like cartoons come to life for a kid.
Walk the kid along the Palace of the Governors - much of the jewelry sold there is truly beautiful. Lots of chotchkie stores around the Plaza. Rule of thumb is that if they are having a sale, what they are selling is junk. The Plaza is a good starting point, but there's a lot more to see nearby.
Railyard area may be fun for a kid. Santa Fe Brewing's brakehouse is there, too.
Sign up for a pottery or adobe-making class. Yelp should point you toward a good one. In fact I bet there are a lot of day camps.
For adults, hire a babysitter and go to 10,000 Waves one afternoon/evening. The attached restaurant is great, too.
Agree with abqtj on Bandalier. Not a challenging hike, but perfect with a kid and lots of cliff dwellings and ladders to climb.
Are you flying into ABQ or SAF? If ABQ, drive up via Madrid. Funky little town. Pronounced MAD-rid.
Lotta great restaurants. La Choza will have a line, but show up 15 minutes before they open, put your name in, have a drink, and wait. Rowley Farmhouse always has good beer and eats and is on the way to/from Meow Wolf.