You can't go wrong in any direction but expect lots of traffic and big crowds in July. In addition to the geothermal sites my first choice would be Yellowstone Falls and canyon. Get an early start in the AM before vistors pour in from outside. Evenings are a good time to park by the prairie where Wolves are sometime seen. Keep kids well clear of the Buffalo and Elk. They are generally very peaceful unless approached too closely. The Madison is a great trout stream easy to get too but not easy to fish for youngsters. July can be hot so am and pm are nicer and less crowded. If you want a nice day hike up one of the taller peaks there is a trail head parking at Dunraven Pass area with a smooth trail up to an observation post at the top of Mt Washburn. The trail starts at about 8000' and is over 11,000ft at the top. Great view of the whole park from there. Take water wherever you go and pack a lunch.
