Families tend to cluster around the neighborhood school of their choice, and going by test scores the "best" public elementary schools are Eldorado, which now goes to 8th grade, and Wood Gormley, which goes to 6th. Of course your criteria may not be schools with high test scores, in which case your choice is broader. The Eldorado community is family friendly, with single family homes & large lots. It's about 20 minutes from downtown Santa Fe. There are many members on this board who post about Eldorado, so just do a search and you'll find all the opinions you need. Wood Gormley is downtown, in an area called South Capital. Homes here are more expensive than Eldorado, and the area is highly walkable - if you know about WalkScores, most streets around Wood Gormley have scores in the early 80% upwards. Wood Gormley itself is about 7 minutes walk from the downtown Plaza.
You have of course also the option of private schools - Rio Grande School & Waldorf come to mind.
Re things to do - I moved here with a 5 year old (now 12) and we've never been short of things to do, and pretty similar stuff to most towns, with of course the added huge benefit of closeness to fabulous outdoor activities. As SanfordR mentions, there is the
Children's Museum, where me and my son have spent many hours! There are also community centers with excellent swimming pools, and private swimming & tennis clubs.
Hope that helps to start your thinking!