The best known (or at least most actively promoted) one is Napoli Sotterranea.

It's not particularly difficult physically (I'm 65 and substantially overweight) though what you mean by "non-athletic" may be different from what I mean. There's one stretch - not where the WW2 shelters are, or even particularly old by European standards - where you have to squeeze for about 50-100 yards through a very narrow and very low tunnel. One claustrophobic on our tour found that bit too much, but there was an undisruptive work-round available for her: she simply had to wait (with a companion and in the light) till we'd looked at the gallery concerned (which was worth the scramble), and the tour carried on. I thought the wartime shelters were about the most boring things underneath Naples, though the ancient Greek bits of Napoli Sotterranea were absolutely riveting.

The ticket office seemed pretty sensible about explaining the problems, and the guides pretty used to dealing with people who found it worse than they expected. Party sizes are quite well controlled (this is the EU, not Mexico)

A number of other buildings and archaeological sites in and around Naples involved underground bits we didn't necessarily expect. I didn't find one that caused any more challenges than Napoli Sotterranea.

Unless you're VERY "non-athletic", you'd be missing the best bits if you let worries about this stop you from taking them. To my mind, the most important things about the Bay of Naples are its 3,000 year seamless thread of human habitation, how much of it is still accessible - and how the amount of accessible subterranean antiquities keeps on growing.

The part we saw--the old Roman market--had no sections where it was particularly narrow.

http://www.flickr.com/photos/mksfca/5932928800/in/set-72157627058744325

But clearly it is not the same tour that flanneruk took.

There are dozens of different buried bits of antiquity in and around Naples, visible in all kinds of ways, from just looking at Metro stations to walking through a trapdoor in a till-recently private flat or walking down into a church crypt.

Michael's photo and description is of what lies under San Lorenzo Maggiore in Via Tribunali. Napoli Sotterranea, the most aggressively promoted underground site, is a couple of hundred yards away, accessible through a ticket office in Piazza San Gaetano.

The best known accessible underground sites around the historic centre are described (with sample photos) at www.naplesnapoliguide.com/Naples,ItalyTravel/naplesundergroundtour. But more seem to get unearthed all the time.