It seems to me that you simply do not trust him anymore. It's difficult to be with someone you don't trust, but you should consider, does this mistrust come from a genuine doubt about his ability to be faithful or a personal insecurity and self doubt. It does seem odd to be on a dating/cruising site without telling you and lying to you about the porn was clearly a mistake, but I'd pay attention to his behavior and if he makes gestures to be open and honest then maybe you can feel you can trust him again. Unless you've seen other reasons to be worried. In my view, porn isn't a reason to be worried either.
"The problem is, there is a gay website that he went to about 2 months ago. It is a gay dating site, and also where men find cruising sites and partners. He said he only went there out of curiosity to see who in his town had profiles on that website (where I used to live, we have been dating long-distance for the last 3 years while I'm in college).
It seems like an excuse, if he wasn't caught would he ever tell you this? Seems very shady to me.