A New Camera for Travel

I am looking for a camera (and lenses) for a trip that I am planning on taking later this year, and I know my Galaxy Nexus won't cut it. I haven't been a big camera user before this, but I would like to lean about the finer points before I go, and have been looking into getting something better than a point and shoot. So I was thinking that either a micro 4/3 or a NEX camera would suit me pretty well as it is reasonably compact but still lets me play around and get some good looking shots and videos but I have no idea what would be good apart from that, or what lenses I should look at getting.

I can spend up to $800, but would prefer to spend less unless the cost is justified.