Well first things first, I won't jump to conclusions and run over to her and the guy and make a seen, that would probably make me look like a stalking insecure husband, especially if there's a reasonable explanation for her being there with the guy.
I'd do one of two things;
1. I'd watch her and see if theres anything seemingly romantic about the way she's behaving with the guy in question. If I don't see anything then the next thing to do would be to call her and see if she'll take my call. If she sees the call and doesn't pick then my suspicions would almost certainly be right, if she picks up the call and I ask her where she is and what she's doing and she lies then I'll know she's cheating, if she says where she is and what she's doing then I'll know that she's not.
2. I'd leave her be and head straight home and pretend like I don't know anything. When she comes to bed I'll ask her how her day went and try to see if I can get her to say that she went to a hotel with someone. If she neglects to mention that she happened to go to a hotel with another man then I'll still try and get her to give me a run down of all she did that day. If she still doesn't mention the hotel then I'm just going to conclude that she's cheating.
If on both counts she fails then I'd confront her about seeing her and make sure that she knows that I saw her and she's been caught. As long as I know that I've been doing everything in my power to be a good husband then honestly I'm not sure I'd remain in that marriage. I'm a firm believer in fidelity and I can't see myself cheating so I won't remain in a marriage with someone who cheats on me.
I hope this helps.
Record the conversation.
If they can convince me it's a nothing burger, then fine.
If they cannot, or confess, I get a divorce.
Pictures and recording are all the evidence a judge should need to rule in my favor.
Or, I would freak out.
Well, whatever I might think I would not jump to hasty conclusions and try rather to find out what is going on. It might be completely harmless.