One Night in London: What's the best thing to do?

My girlfriend and I have planned a trip to Prague and Budapest, but on the way back we have a night time stopover in London. Our flight arrives at 10:40pm, so we're not sure if we should:

• Grab a hotel room. I'm not sure if I can make the Tube into the city, or if I'd be stuck at the airport all night.

• Go into downtown, find a club, and hang out all night.

• Which place in the city is the best to be in at night? If we find a good spot in the city, I want to make sure I book a hotel near where the club/bar is, so we can drop our bags and head out.

• Find some Redditors to hang out with, or maybe someone that's willing to accept late-night couchsurfers.

Specifically, I need to know the best way to get to the city, as from what I've found the last subway car leaves Heathrow at 11:40, and I don't want to be stuck at the airport if I have other plans.

What should I do?