"If [the Universe is finite], what is beyond where it ends?"
There are two valid answers to this: no idea, and nothing. I can't particularly comment on the first option (pick your favourite version of M-Theory), so I'll just leave it. However what is true is that the logic that led you to ask the question in the first place is a little mistaken, relying as it does on conceptions of boundaries that are a bit too three-dimensional.
Essentially the point is that there is no place you can stand in the Universe that you can call a boundary, at least not a preferred one. And that already makes the concept of "beyond" misleading. There is no beyond. There is no need for it. In the same way, the Universe doesn't have a centre point (or at least again, it doesn't have a preferred centre point. You can't draw an edge, and you can't find a centre. In that context, you can't even frame the question about what lies beyond. It doesn't really make any sense.