you can easily drive to Cody once you start the trip

For flying to that area, no way one should fly to Cody - even if it has commuter plane services - the fare would be expensive and the flights very few, plus not very safe.

Here is what I would suggest - you can make several loops inside and outside park. In our trip one day we left park from the Northeast gate (Beartooth was still close in 2005, probably would be open in 2007), and took Chief Joseph Scenic Byway - by far this is the most scenic drive in the area althoug it is outside park - towards Cody and re-enter the park from the East gate in the evening.

We have been thru every gate of the park, West, East, North, Northeast during our 5 day trip (the last night was spent in Jacksonhole).

One word of caution - strongly suggest to buy optional insurance w/rental car because of potential weather damage. We did not buy it and we came accross hail storm when we spent a night just outside North gate at Gardiner. MT. The end result was, my credit card (MC) insurance paid $2282 repair estimate, we paid $350 loss of revenues and admin fee, not to mention a lot of headache - it could have been avoided by paying $16 a day x 5 days extra insurance.

Search my name you will find my post for this experience - it is quite a learning experience on HOW TO deal with this and eventually get the insurance settlement.