I went there 2 years ago, to both Grand Teton and Yellowstone. Both parks are awesome (I took 1200 pics on my 2 digital cameras <img src="/ubbthreads/images/graemlins/ooo.gif" alt="" /> ). It was one of my favorite trips. I recommend hiking the trails and getting off the boarded walkways and away from the crowds. We had some amazing hikes and saw lots of wildlife and scenic views by hiking the trails. My favorite hike was hiking to the top of Mt. Washburn. It is a steep hike and about 3 hours or more each way but well worth it. <img src="/ubbthreads/images/graemlins/smile.gif" alt="" /> Plan to spend a half day hiking it if you decide to do it. We also drove all the spokes to see the entrances which made for some nice scenic drives. All of the main sites are nice so I recommend seeing as many as time allows. How long are you staying? We did 5 days in Yellowstone and 2 in Teton and that seemed like enough time.
If you have any questions that are specific, let me know. You will love both parks - they are simply awesome.
Just make sure you do the common sense things if you take the off-the board-walk type hikes. Take food and water, sunscreen (it was mid 90's and very sunny when we were there), chapstick or something for dry lips unless you are accustomed to the dryness, maps or guides if you have them, hats and sunglasses, and most importantly --> Grizzly bear bite salve. <img src="/ubbthreads/images/graemlins/laugh.gif" alt="" />
Have fun!