Are all of the ball joints and bushings in the front end tight?  The 86-89
accord will wear out every ball joint it has at some point or another.

I'd be focusing on

(1) tires. Are they properly inflated? The correct size? Evenly worn?
(2) suspension problems

Maybe take the car into a good shop for a complete inspection of tires, ride
height, struts, ball joints, wheel play, etc.

I'd hold off on having an alignment done just yet because of what an article in
the July 2004 issue of "Import Car" said. It discusses the basics of Honda
suspension and steering problems. If you want to read this 4-page article, go to
http://www.import-car.com/ , then click on "Search Back Issues," then put in the
key words

Dowie AND suspension AND steering AND diagnosis

The second hit is the article "Honda Suspension System Diagnosis and Service,"
by Bob Dowie, Import Car, 2004.

The article notes that
-- a common suspension failure point is where the sway bar connects to the
control arm.
-- Also, bushings that mount to the chassis may become loose over time.
-- Lastly, front lower ball joints are common replacements on (older?) Hondas
-- Only the alignment angle "toe" is typically adjustable on Hondas, but it
won't usually cause handling problems on them.

Updates welcome! I for one am trying to get some experience in this area.

Good luck.

Check the bushings in the lower A frame.

I am having the same issue with my car (a 1998 Integra). Did you ever
figure this out..?

Was it a sway bar loose, a bushing? a ball joint?

Please let me know
Elie.