いっしょに　かふぇに　いきませんか？ / Shall we go to a café together?

いっしょに

It means "together".

かふぇ

It means "café".

いきません

this means "don't go".

いきませんか？

this is a question form because "か" is put at end. This means "don't go?, shall we go?" with which you can ask someone to go. The reason why this is negative form as "don't go?" is, that it is easier for the listener to answer no to this question. You usually ask in this way.

いきますか？

this is in a positive form. this is also correct. It means "go?, do you go?". It's more expecting the positive answer from the listener. However, the above negative way is used more often.