Suggestion for carrying a tripod: on a shoulder.
If you have room for everything take everything. ND filters, polarize-rs, wide angle, telephotos, macro lens, extension tubes, memory cards, extra batteries, back-up camera, lens shades. I use a belt system and a vest combination. For hiking and transporting I use a camera backpack at 35 lbs(not including water or food) !
What to see: Upper & Lower Yellowstone Falls from every viewpoint. Old Faithful Geyser, and Geyser Valley, Yellowstone Lodges, Yellowstone Lake, Lamar Valley: Antelope, Bison, Wolf, Bear, Gopher, Moose, Elk, Pronghorn. Fire-creek Falls. Also take a day and drive to Grand Tetons NP just south of Yellowstone, the best time of day is early morning light. But shoot throughout the day....it's a paradise! I was there 1980, 1990, 2001, 2005, 2008. Every time we tent camped! Good luck, bring back plenty-o-photos! Treat everyday like it's the last day and you won't be disappointed! Use every ASA & be creative. Don't be satisfied with one shot!