I'm sure Starbucks offers something other than ONLY coffee drinks... tea or hot cocoa even? I have never been to a Starbucks myself (due to lack of availability and I am like you... dislike coffee!).
However, it is FINE to have agreed to meet at the Starbucks. If NOTHING else, you can ask for a cup of ice water, and buy a biscotti or something to go along.
When you are finished with your introductory chatting, simply tell your lady-friend, "Now that we have the coffee done with, would you like to go for some lunch?" (or a ride, or whatever the next activity may be)
If she asks why you are not drinking coffee, you happily tell her, "Oh, I don't really care for the flavor, but that's okay! They have great water (cocoa, tea...whatever) here, too!" And just move on with the conversation. Not everyone likes coffee, but Starbucks just happens to be a good place to meet people and such. There's no shame in it.
I'm lucky that my boyfriend does not care for coffee either. But even if he did, I have no problem in his having "his" drink (which he does anyhow... LOVES Dr. Pepper!) and I mine... iced tea!
Have a polite day.
Etiquette takes over where laws end.