I'd appreciate a little advice re an upcoming leisure trip to Tokyo if I may....

A little background - my wife and I are fairly seasoned travellers, and whilst £££ is not a primary consideration I don't want to be spending a fortune either!

1) We are flying LHR - HND and arrive 04.55. I have provisionally booked a hotel that got good reviews on Booking.com, the Annex Katsutaro Ryokan. This is apparently by Sendagi subway station. Given that we can't check in until 15.00 hours, what would the suggestion be for using this time wisely, especially given that we'll be a little tired.... I am guessing presumably a couple of hours at least through customs/immigration and into town.

2) Reading through this forum, I get the impression that for the short time we are in Tokyo that any major trips outside of the city are probably a waste of time. Would I be correct in this?

3) Haven't got the guide book yet, but what do people think are the "must do's" in this timescale?

Once again, thanks for any input you can make.