1998 Accord vibration

Recently I started to get a vibration in a 1988 Accord. The car has 65k miles
on it. I'm pretty sure the vibration started suddenly and was not something
that gradually got worse. As you approach 55mph the vibration starts to be
noticeable. Sometimes the vibration will go away for a little bit and then
come back. I did notice that if I accelerate, the vibration goes away until
I reach a steady speed, then the vibration comes back. I already tried
swapping the wheels front to back and also got all the wheels balanced, the
vibration is still present, although it seems to have lessened a bit after the
balance. This weekend I'm going to take a closer look at the car. Anyone
have an ideas on where to start looking? TIA