Well, it has to be slightly more complicated than that. After all you are going to be emitted as hawking radiation a lot earlier than the end of the universe.
Large black holes have life expectancy so much larger than universe age that it's not even funny. They're not going anywhere AFAIK. No, you will stay there and watch.
"The power in the Hawking radiation from a solar mass black hole turns out to be a minuscule 9 × 10−29 watts. It is indeed an extremely good approximation to call such an object 'black'."
Larger than the current life of the universe, not necessarily longer than the end of the universe, though that really depends on your model of how it'll all end. Some do involve black holes gradually boiling away to radiation being the last things being left.
If spacetime continues to accelerate its expansion, a black hole at the future end of time might be like suddenly dropping the air pressure over a boiling pot of water--or maybe more like popping a blackhead pimple by stretching the skin on either side of it.
I am not a theoretical physicist, though, so whenever I think too hard about how that would actually work, I give myself a headache and need a good lie-down in a very dark room.
