Hugs are totally fine for 2nd date, man. But you ought to give her a kiss the next time. It can just be a drawn-out peck, no need for tongue.
The most important piece of advice I have for you is: Chill. Guys have a bad habit of smothering their new girlfriends with attention. I think you should wait a little while before the 3rd date and see if she asks you somewhere. If she's old-school and always waits for your move, then go ahead and get another date.
The point is, you want to strike the right balance between taking the initiative and not appearing needy. You want to make her feel like she has to compete for your time and attention.