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While sitting and chatting sounds perfectly reasonable, it can be really awkward on a first date when the two of you are trying to figure out what you have in common to talk about.
So, anything that gets the two of you active together will be less awkward than sitting across a table. Sometimes doing the tourist thing in the town you live in can be fun. The planetarium, the zoo, MOMA, MFA, etc. Why should tourists have all the fun?
You might get some more tailored ideas by striking up a conversation about being a little bored, and ask her what she does for fun when she isn't working. If she's a reader, a trip to a used book store she's never been to might be good.
Glad you made the decision to ask her out. Hope all goes well !