We had a similar flight time. Departed SFO about noon, arrived 2 pm. The time on the flight was our usual awake time anyways, so I think I only napped a little. I didn't have to purposefully keep myself awake. By the time we got our luggage, through customs, on the train, to our hotel, it was sometime after 4 pm. We unpacked, had dinner nearby, then early to bed about 8 pm. The flight time worked out well for us.
The kids woke up at an unholy hour of 3 am, but I was able to get them back to sleep eventually. The first day, I planned it to be easy, just walking around Asakusa, where we were staying. Everyone needed a nap in the afternoon, we had dinner, then early to bed again. I think if you're adults only - you can probably power through this day. The next day, everyone was fine, except I had a bout of tiredness in the evening.
I was worried about the jet lag too, but it turned out way better than I expected. Coming back was a whole other story though! Our flight home arrived at 8 am. When we got home, I was soooooo tired, I was asleep the whole day.
It took me a long time to get over the jet lag - so that would be what NOT to do.