Hey Dino! Good news there! Now, whatever you do, don't blow it! She's now friendly with you, so I'd back off just a little bit. People keep saying it, but it needs to be repeated: DON'T SMOTHER HER!! Just let things develop as they happen. Read her reactions all the time, and adjust your behavior accordingly.
It sounds like you're doing great so far. Don't worry about forcing a date to the cafe in there. That might be too much too soon. However, if she brings up wanting to do something, that would be a good time to ask. Or if you two start becoming good friends, then ask. Hey, it's always easier to ask if a group of people are going. Then there's not so much pressure.
Good luck!
Capslock