I got a 1980 Fuji bike yesterday in otherwise great condition cosmetically and mechanically, and it rides fine.

However, the wheels are not centered - both sit to the left (if you're riding the bike) in the fork and in the rear stays. I haven't checked the rear stays, but I checked the fork with a level and both blades appear to be in line with the head tube. The steering tube I assume is fine, because there is no play or binding when turning the handlebars. I then checked the dish of the (front) wheel out by putting it in another bike (that I knew to be fine), and it centered. To me that suggests that there is no problem with the dishing.

Could it be an issue of the fork/stays being bent out or in rather than back or forth?