You should say:nice to meet you too!

you too

I asked about this one before. The answer was: When you say "you too' it means that you are returning the compliment. What you are saying to them is that you liked meeting them too. But when you say 'me too' it is like saying that you like meeting yourself.

You can say "Nice to meet you too."

you should say "you too"which is short for "nice to meet you too".