With friends "let's" is more natural, in The UK and Shall is good also in this informal situation. shall is asking a question? let's is making a suggestion. And shall is refusing to die, in the UK, it is used more often in America than people admit, but it means "will" in both the UK and America. Except in old vintage literature in The UK.

I actually thought the same as Brandon, wrote this, then decided that it was not actually so after all. "Shall" is not really the first choice nowadays, but I thought, talking with friends, it seems fine for such an informal question. Let's ... seems to suggest that we should and seems therefore more leading an answer of "yes". Shall we, in this sort of use seems quite natural and neutral, as if the place is the suggestion. . How about, we get together ....also an option, butr again leading.

Grammatically, all are fine. However, the tone of "Shall we...?" questions is a tad more formal. This may be a US-UK difference, but I wouldn't use "Shall we...?" with friends myself.

I would say so.

All good.