Keep it simple. You have some situational comfort/rapport with her from class and the few minutes you spent talking to her. You can get a date from this without a doubt. but you can't make it an awkward meeting location.
If you invite her out for coffee or dinner she is thinking of forced conversation, and awkward silences.
Invite her out to do something! Like: Go Karts, Mini Golf, Bowling, Shooting Pool, Laser Tag, etc. (Not Movies) This way you have something to do while you talk and it's not as weird.
Make it a simple message to her: "I'm heading out to one of my old stomping grounds.... OR I"m heading to one of my favorite hangs... at the Go Kart Track. Do you want to tag along?"
This way if she says no you don't loose any face and you can always say you'll have fun anyways. If she agrees then great!
GOOD LUCK!