Fly in, and stay outside the park where the rates are going to be cheaper. Staying in Gardiner or West Yellowstone are also going to be expensive, but still cheaper than say the Old Faithful Lodge. Get a rental car and make the drive to the points that you want to see each day. Makes for a longer day, but it can be done. (I used to live in the Bozeman area, and managed to see almost all of Yellowstone just through day trips)
Another option is to camp in the park. Check the campgrounds out, there are some that are "hardside" campers only because of the bear activity, but there are those that will allow tents. The camping fees are MUCH less than motels, and add a bit of adventure to your trip, especially if you've never camped before! :)