I asked this girl to go out for some drinks, but I can't think of any places. Any ideas?

Try a restaurant that specializes in appetizers, or tapas or small plates, as opposed to a restaurant that is more of a fancy sit down place serving a full meal, but at the same time is not just a bar. Or go for wine at any restaurant, but just go for wine and dessert (instead of dinner). It will be much more casual.

Where do you live?

The tapas idea is good.

I would say go somewhere that the music is not too loud so you can talk easily if you go to a bar.

Tapas is a great idea! Some place like this.

Or this

You could always ask her where she would like to go, but have a backup place in mind if she decides to let you choose.

Great ideas thanks y’all. :)

It would help if you gave us a clue where you live.
I really like those fondue places. Depending upon the time and intent of the date you can get cheese fondue – or chocolate. The whole meal can be foreplay.

See, I would not be keen on fondue for a first date. I want to have total control over the size of the bit of food, and fondue tends to be cut for you and you have to shove the whole thing in your mouth.

But everything tastes good when it’s covered in warm chocolate.

@LuckyGuy On my first date I am worried about how I look, not what the food tastes like. I don’t want to have to crack anything open, try anything new, chase anything around my plate, or have a high chance of something dripping. Yummy food helps, don’t get me wrong, but I would not want something unusual or hard to eat. I don’t want a new dining experience on my first date, I want a no-brainer, I can focus on conversation, meal. That’s just me. Meanwhile, the OP just said drinks, so food is not the main gig, most likely she won’t be very hungry if she was invited for drinks.

@JLeslie I never order spaghetti in public for the same reason. I couldn’t tell if the OP was asking for a first date idea or not. He was asking for some place classy and relaxing. The morsels that go in the fondue are bite sized and the ‘due sticks quite nicely on the stick .
It’s a small adventure.

@LuckyGuy I cut my spaghetti. The twirling with marinara is the real risk.

I had assumed first date, I could be wrong. If you are ever in Memphis I’ll go to chocolate fondue with you. With my husband along of course, not a date, just saying I am willing to fondue depending on the situation.