Is it illegal to merely set foot in one - even if the establishment displays licenses and such?

AMPs are legit.
that's like saying it's illegal to step in a strip club cause some girls offer extras, lol.  

there is a level of plausible deniability. Cops have questioned people coming out of an AMP....but don't give away info....just say you got a massage. if they ain't making a bust while you in the AMP engaging in activity you have nothing to worry about as long as they are licensed.

Whether or not the prosecution went through (I can't believe it did... anyone know?), in recent NOVA raids the patrons were charged with "frequenting a bawdy house" and named in the local press. ie they were charged with just being there.

They can arrest you, throw you in jail overnight, publically shame you etc etc without ever pressing a charging on you. Heck, they can even do this even if you as much as look in the general direction of AMPs. You may be able to shell out bucks to hire lawyers to get you out, but it would be after your reputations and relationships are ruined.

It isn't necessarily illegal to set foot in one. If it were, then logically - it wouldn't be legal for the places to exist.

The poster who talked about visitors who get charged with frequenting a "bawdy place" is correct - that is generally the charge. The specific code section for this in Virginia is 18.2-347. It is important to note, however, that per the code - it is only illegal to visit a bawdy place for an "immoral purpose."

So, in other words, stopping in and asking for directions is presumably ok