You can fly into Jackson, WY, or W. Yellowstone, but the cheapest way is into SLC, get a car and drive the 5 or so hours. Accommodations inside the parks are either very expensive, or very rustic. Or some of both. You can camp, but reservations are essential. I'd suggest timeshares outside the parks. There's a Worldmark in West, a couple in Jackson, and Island Park, ID, 20 miles out of West. Maybe stay 1 or 2 nights at Old Faithful Inn, or Jackson Lake to get the feel of the places. There are tons of 1 to 3 mile day hikes you can take. There are good guidebooks, and online info you can chase down. The season ends at Labor Day and the parks start shutting down, so 'fall' happens early at 8,000 feet.
Jim