Various good suggestions above, my input would be yes, go into the city and walk around, have dinner somewhere. Where you go, what you do, and how long you stay will depend on weather and how early next morning you fly. But don't just sit in an airport hotel if you have the chance to experience a bit of London for the first time.
Mrs. EB is right that the Heathrow Express will get you into London much faster, and that advance tickets (for a particular day, not a particular train) can save you a lot of money vs. the walk-up fare. But the Express will put you at Paddington Station, which is hardly the best jump-off point for the heart of London. You'd have to take another tube to the area Claudia and Jen describe, which I agree would be your best place to emerge from underground. So the Piccadilly Line to Leicester Square would be the simplest way to get there, though perhaps slower.
It will be dark, so just take a walk and find a pub for dinner and maybe a pint. You'll have lots of choices. Get a map, either a free simple one from a kiosk or an inexpensive good one like Benson's. You won't see everything, but you'll get a feel for this great city and start thinking about returning for a real visit. One key warning for pedestrians -- remember that they drive on the left, so LOOK RIGHT before you step off the curb. Requires constant alertness on a short visit.