The mechanics suggestions make sense, but get a total estimate and compare that to buying a modern bike more suited to your needs, either new or used. Bikes have improved tremendously since 1980 and you get much better product for the same dollars. If you shop around you can probably find something nicer than your old wheels for $350 new or half that used.
When comparing the cost of upgrading vs replacing, also allow for other stuff that the old bike might not need today but will soon enough, like new tires, possibly a saddle, bar tape, etc. If the price gap gets narrow, go new, it'll cost you less over the course of the 1st year, and you'll be riding nicer stuff.
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