Cody was mentioned above because of the rodeo but, also, the real draw is:
Buffalo Bill Historical Center A fascinating and world class complex (with cafeteria); plan on at least three hours. For all ages. http://www.bbhc.org/home/
And more of an art museum, in Jackson Hole, also well worth visiting:
National Museum of Wildlife Art – Another remarkable museum. North of Jackson on the road between Jackson and the south entrance to Grand Teton National Park. http://www.wildlifeart.org/
If you go to Cody, plan a possible overnight; the drive there and back is long enough to do so, it's a pretty drive (and you'll have a couple of routes to consider), you'll need the time there to enjoy the town, and you do not, do not, want to drive in the dark; wildlife!
You'll want to reserve lodging inside, if that is your choice, the parks as soon as possible including: For Grand Teton National Park Lodging there might be several, but definitely www.nps.gov/grte/planyourvisit/lodging.htm
For Yellowstone, a lot to consider but it is important:
Lodging Inside and Outside YNP
For lodging INSIDE the Park - http://www.travelyellowstone.com/ Xanterra is the YNP contracted lodging resource. Other agencies might charge a nonrefundable service fee and they have to contact Xanterra themselves which you can do for free.
To get reservations in the park - (1) Monitor the Xanterra website continuously, and if you can, (2) CALL, at least once a day as cancellations often occur. Lodging and dining locations, costs, reservations, camping, tours, things to do and much more are on the Xanterra website.
If you find nothing available in the park when you call (the website is rarely current), reserve lodging outside the park but know the cancellation policies. If you later get Xanterra lodging, cancel those reservations.
For lodging OUTSIDE the Park - If you cannot get or do not want lodging inside the park, use the gateway towns of West Yellowstone and Gardiner, both in Montana. See the hotel reviews on the TA Forum for each city, left hand column, “Hotels”. Ensure that your lodging outside the park is close to the entrances; you won’t want to add many miles to your trip, you’ll have plenty of miles in the park.
SPLITTING Lodging Locations – The park is vast so if you have 3 or more days, consider two lodging locations to minimize driving. Also, proximity to lodging could be safer because wildlife is very difficult to see after dark.
Consider any of the following combinations, depending on what is available and the type of lodging wanted. See the official park interactive map at http://tinyurl.com/6tp6kvh to understand these locations.
• Old Faithful and either Canyon or Lake
• Old Faithful and Roosevelt or Mammoth or Gardiner, MT.
• West Yellowstone, MT and either Canyon or Lake
• West Yellowstone and Gardiner.
Edited: 17 May 2012, 4:28