Take the NEX. It goes directly to Tokyo Station non-stop, from where you can easily stroll into Ginza. Green car (first) is a little under 5,000 yen per person each way. Regular fare is about half. It takes just under an hour.

You can probably catch a train around 10:18 which will get you to Tokyo at 11:19. For the return, catch a 13:33 train which will get you back to Narita at about 14:28. (If you miss that train there is another one around 2:00, which will get you back in time).

Customs/immigrations/security are very straightforward and won't take more than 15 minutes each way.

There are no significant safety issues.

I would avoid the other trains as you have to figure out which train to get on, which stop to get off, and sometimes where to transfer. NEX is easiest and fastest, but more expensive.

You can walk along the Imperial Palace and then the Ginza shopping district. I'd probably skip lunch as you don't have a lot of time.

You should have at least 30 or 45 minutes in the lounge before you're flight to SFO.