You want to go out with your new Greek friend or you want to ask out that Greek guy or girl you met the other day that you cannot stop thinking about! Here are some phrases to help you out and I think that you will be successful!

You will use the the 2nd person of the verb «θέλω» so «θέλεις» or «θες» = do you want. Then you will have to add «να πάμε» = (for us) to go plus «για» and the noun like: φαγητό, καφέ, ποτό κλπ

θέλεις + να πάμε + για (ένα) ποτό αύριο το βράδυ;
Θέλεις + να πάμε + για φαγητό την Τετάρτη;

Or even without «για» in phrases like:

θέλεις + να πάμε + σινεμά;
θέλεις + να πάμε + μια βόλτα;

If you want to do something then after «να πάμε» you add the verb again in subjunctive mode, so the phrase would be:

θέλεις (θες) + να πάμε + να χορέψουμε; = Do you want to go dancing?
Θέλεις (θες) + να πάμε + να φάμε κάτι; = Do you want to go and eat something?

if you want to invite more than one person, then you have to change «θέλεις» and put the verb in the 1st person plural, «θέλετε».

I hope that was helpful! Good luck!