Might seem odd to some people, but something my father and I have done several times is go to Jurassic Park Discovery Center. What we do is go to the area where it says "Beasaur", where the dinosaur figures are downstairs. We sit down and lean against the rocks. Sometimes people might be over there, but for the most part, typically there isn't many people in that area, or most times no one at all. So, it's a nice place if you just want to relax in a nice air conditioned place.
Also, a place I noticed recently, but have never personally used to relax, is the hallway that Horror Make Up Show exits into. After the show, the doors open, and you walk into a hallway, then you can go through a gift shop (a gift shop that also is used for an exit for Terminator). Once again, a nice air conditioned place, more, or less relatively quiet, and for the most part hallway would be empty (except when Horror Make Up Show ends and everyone exits). So, about every 45 minutes you get some visitors who will quickly walk through the hallway. Other than that, I think it would be a nice place to chill and I personally do not see why an employee would have an issue (besides I doubt they would notice).
There are plenty of places at resorts I would imagine, but I wanted to mention the two air conditioned places that I know of (one for each park) in which you could relax, relatively without no interruption.