In most cases, one can fly VFR in the U.S. without any flight plan. However, if you are crossing an ADIZ, it is my understanding that you have to file a DVFR flight plan.
Consider an airport such as KDGL (Douglas Municipal). In theory, it looks like one could fly to the airport from the north without ever crossing into Mexico, but as soon as you need to do a go-around you would be crossing the U.S. ADIZ into Mexican airspace (and crossing back into the U.S. when returning to the airport).
Do you need to file a flight plan (or any other paperwork or paying overflight fees) when flying to such an airport? Do you also need to file a flight plan if you are simply flying the pattern at the airport?