If you are going in July/August then just be prepared for a lot of elevation gain. Weather is the main thing to keep an eye on, start very early and start heading down at the first signs of storm potential. Don't go onto snowfields without proper gear and the ability to self arrest.

If you are considering a peak, consider South Teton, Middle Teton, or Teewinot. If something more mellow, Amphitheater Lake gets you up around 10,000 feet with nice trail the whole way. Bring bear spray and know how to use it. Watch for huckleberry bushes - they are everywhere and have fruit that is delicious to the taste.