Marlin's giving some good advice, too, with a good point about the timing belts on Hondas. BUT, not all Hondas are interference engines! The carbureted 2.0 on the 86-89 Accords will do nothing worse than strand you if the belt fails. Note that this is the engine in the DX and LX, but not the LXi or SEi.
I can tell you, if you're lucky enough to find a dealer maintained 86-89 Accord that's in good shape, you've got a winner. I found just such a car, an 87 Accord LX with 208,000 miles, so I bought it for $600. I took pretty good care of it, like I would any car that I need to depend on, and I got 40,000 miles out of it (would have gone a lot farther, but I had an accident). The most major repair it required was a water pump, also the original exhaust pipe between the manifold and the cat went out. It already had the rest of the exhaust replaced with new Honda parts (Stainless steel, I believe) the year before I bought it, and those lasted fine.
EDIT: The reason I mention a dealer maintained Honda is because some mechanics will put really crummy, cheap parts on a Honda, and that basically ruins the reliability. Honda OEM parts (from the dealership) are the way to go in order to keep a Honda running like a Honda.