If you want to ask someone to go have coffee with you, the simplest way is probably to ask:

Veux-tu aller prendre un café?
Voudrais-tu aller prendre un café? (seems a little more hesistant)

You’re asking if they want to grab a coffee. The part about sitting down in a coffee shop and talking is implied.

If you want to ask someone if they want a cup of coffee, like offering to get one or even pay for one, you can say:

Veux-tu un café?

If you’re at home and have the means to make and/or pour coffee, you can ask if they want some coffee:

Veux-tu du café?