I'm currently in the exact same situation. I met her last week, tomorrow I've a second date.
This is what I'm thinking: If you like this girl (otherwise you wouldn't have asked her out before) and she obvious likes you, what is the problem? Just ask her out, she practically already said yes by excusing for being in that other city. And why can you only go on a date in the weekends?
Don't let her know you don't know which city she been. If it was a fun trip just ask where she's been or what she saw.. Though I don't think it will come so far, I think she will drop it herself.
I hope to hear how it ended mate, I'm gonna have a great time and I hope you have the same
