I bet you could find the answer in a library. Start with design annuals, then move on to books about advertising in the 80s, and from there to microfilm catalogs of 80s magazines and newspapers.

I agree, ITC fonts like ITC Souvenir, ITC Cheltenham and ITC Avant Garde all seem to be solid choices.

ITC Garamond and ITC Berkeley especially have the fine details for display.
Make sure to set them reeeeeeeal tight.
In fact, that style of setting is more significant as a marker of the era than the choice of typeface.
This from Typsettra:

But that tight look for headlines, which began in the 1960s, was passé by mid decade, replaced by heads that were tracked out.

That was for mainstream.
Alternatively, Punk was the look 1977-1984, with collaged heads where many fonts were mashed up in the same sentence.
Again, mid-decade, that changed. Neville Brody introduced Industria in the London scene magazine The Face in 1984, heralding a structured look.

So there you have it, four "eighties" type looks, depending whether you go straight or alternative, early decade or late.

As a manufacturer of film fonts during the 80s. I found Handel Gothic Bold and Light a popular seller. Faces like Blippo Bold, Yagi Double (CNN logo) were also popular. Some of the basic display fonts had added swash characters. Alphabet Innovations had some very popular franchised fonts.

Thanks everybody! This was really useful since I didn't really have the time to do some serious research at the library...