Recently ‘they’ found a brown dwarf nearby. A brown dwarf is a star that never quite made the grade; when all the other stars in the dust cloud were snatching up fuel these hapless wanna-bes were left just shy of the mass (and therefore gravitational pressure) to squish hydrogen atoms together into helium, and as a side effect shooting off heat. They’re barely stars at all.
You can see a thoroughly uninteresting photo of one over at Astronomy Picture of the Day. It’s pretty close to us — on a cosmic scale at least — a mere 40 light-years away. What made this one interesting (to me at least) is the surface temperature. It’s about the same temperature as the room I’m sitting in right now.
So let’s say, for the sake of Science Fiction, that one can travel faster than light. Only slightly more impossible would be dealing with the high gravity. Once those two minor things are taken care of, you could build your house on this star. Well, there probably isn’t a real surface per se, and there’s likely to be some pretty wicked radiation and magnetic what-not. And epic storms, like on Jupiter.
BUT – if you solved those things, you could build your house on a star. That would be cool.