We have an event horizon 13.7 billion lightyears away in every direction. So we're in a spherical volume surrounded by an event horizon.
Beyond that is the rest of the Big Bang, which is thought to be something like 10^21 lightyears in typical radius.
The geometry of the Big Bang as a whole is likely to be a 4-dimensional hypersphere with a characteristic radius of around 10^21 lightyears. That means, if you go straight in any direction at infinite speed, you wind up back where you started after a journey of around 10^22 lightyears. (The analogy is traveling in a "straight" line on the surface of the Earth, eventually you go around and get back to where you started. Don't forget--- space is curved. Also, I say infinite speed because the whole thing is expanding much faster than light and so if you were going at the speed of light you'd never get beyond even our event horizon.)
That 4-D hypersphere that is the Big Bang may or may not be embedded in an exterior manifold of 4 or more dimensions which may or may not have more (perhaps infinitely many) other Big Bangs within it, extending infinitely backwards and forwards in time.