We arrive at Heathrow around 3pm and will stay at a hotel near the airport. The next day we will check out of the hotel by noon. Any suggestions for a night out that's not too expensive or complicated to reach. Thanks!
The Piccadilly Line underground will take you from the airport to the West End of London and back quite cheaply, and runs until just after midnight. If you get off at Piccadilly Circus there are lots of restaurants and pubs around, and many of the top theatres if you want to book a show in advance.
If you don't sleep on your flight from California, you could be too jet-lagged to attempt Philip's suggestion, but it's certainly worth a try, if you don't have more time planned in London. (If your first destination actually is London, then don't sleep at the airport.) There certainly are restaurants near Heathrow Airport, which you can find on Google maps or with the advice of your hotel.
It would help to know what your other plans are. Are you doing this on arrival from the States, or will you have been elsewhere in Europe when you arrive in London? The previous poster is right in saying that if you are arriving from the States on that day, you most likely won't make it very late into the evening before you crash, but you could go into the city for dinner.