If, as you say, you are planning on going out for dinner in SFO in the evening. I would definitely get some rest on the flight.

Have a nice meal, watch a film and enjoy First Class and then have a few hours sleep, then you will have the energy to go out in SFO and will then be ready to go to bed at a normal time in SFO.

However you will wake up in the early morning, the first night, no matter what time you go to bed!! If you do wake up early, as I am sure you will, best to keep the lights off, as the moment you turn them on your body will completely wake up, and try and sleep in till a normal SFO breakfast time. Then hopefully you will be on SFO time. You will start to flag in the afternoon of the first day but don't be tempted to have a nap that day as this would put you onto UK time again.

Hope you have a nice trip.