For suggestion at Grand Teton Nat'l Park, look at this park web site. Also, all the national parks have a site like this with lots of good information for things to do, camping, roads, special alerts, etc. Click on all the topics - lots to do. One thing we really enjoy is taking a gentle float trip tour down the Snake River in the park. You just might see a moose in the water with you. We did!
http://https://www.nps.gov/grte/plan...activities.htm
In many ways we enjoy the Tetons more than Yellowstone although we've been to both many times. The Tetons are like a mini-Alps with wide open vistas. The hiking is superb - even the easy ones. If you carry bikes, there's a terrific bike trail, paved and off the road. The ranger programs are great. Take the chairlift up the ski hill for a great view.