Just some notes that haven't been fully covered....

80s touring bikes with cantilever brakes were typically (always?) built with 27" wheels. It's an obscure size now, but there are enough decent tires out there. Panaracer Paselas are the most recommended here and they tend to run large. Their 27x1 1/4 is likely the largest road tire you'll find for a 27in wheel. To be fair, it's pretty big.

If you want even more clearance, a 700c conversion is in order. If you're really really lucky, it'll just be a drop-in-and-you're-done conversion.
The biggest problems typically come when dealing with canti brakes (which most good touring bikes post-1983 had). Canti posts were placed closer together then than now, so a lot of modern brakes just won't work, period. If you're lucky enough to have stock brakes or find new brakes (there's one model in particular that seems popular for conversions, but I can't remember off-hand) with enough adjustment to reach 700c rims, expect a reduction in braking power nonetheless. The angles of it usually just don't work out in your favor.

Of course, if you go for a sport-touring model, a lower-end touring model or a touring bike made prior to 1983, chances are you'll have caliper brakes, which make conversions so much simpler. If your brakes don't quite reach 700c rims, you should be able to find longer reach brakes no problem.