When you go to Jenny lake, take the ferry across to Hidden Falls and Cascade canyon. It is a short 1/2 mile hike up to the falls and another 1/4 to 1/2 mile hike up to Inspiration point...you could also hit up the Jackson Hole Mountain resort gondolas which take you to the top of Rendezvous peak just south of the National Park boundary, or ride one of the gondolas at Snow King resort which give you a great view looking up the Tetons from south to north.
That day at Yellowstone is going to be a doozy...you better be headed in at daylight if you really want to experience all that. Wildlife will be all over...you don't have to drive up Lamar to see it, but the views up the valley going up toward the Beartooth are spectacular. You can drive up Lamar on your way from Yellowstone Canyon to Mammoth...and also don't miss Tower Falls on the way.
I love the Bozeman area, and it ain't Yellowstone or Jackson Hole...but you will have a blast. We are not much on visiting towns on our trips, we focus on the parks and historic sites.