I was in japan 3 years ago and loved it, i really want to go back but money issues have been stopping me.
I was there for 10 days, spend 5 days total in tokyo, a few days in kyoto and a few days in hiroshima, and there really wasn't enough time to see everything we wanted to see, but it was a brilliant way to see a mix of old and new japan.
If you are planning to move around the country using the rail passes to their full potential and not just stay in Tokyo then i have a few places that i can recommend.
Firstly if you go to Hiroshima then check out the A-bomb memorial, it's quite something to see and hours pass by without you realising it, it's deffinetly very thought provoking.
Another place to go is Miajima, it's about half an hour train journey out of hiroshima and then a freey ride across to the island. You can use the JR Pass on the ferry to get there so it wont cost you anything additional for that. Miajima is home to the
Itsukushima Shrine which is seen in loads of iconic pictures of japan. It's a brilliant little island to explore with shrines etc, has a really wild jungle to walk through (
a pic i took), monkeys at the top etc. It's a fair bit of walking, but if you walk to the very
top it's well worth it, you can see the entire of hiroshima bay from there, and while we were there we were watching the warships and subs come into the harbour from there.
If you go to Kyoto then i would recommend going to Nara, it was japans first capital city and really illustrates what ancient japan must have been like. When you get there you might wonder why there are deer wondering around freey in the roads and parks and it's bacause they are a sacred animal and protected there. The city is basically on a massive hill side and the stuff you want to see is higher up the hill, so we took a bus up there. Here are a few pics i took
1 2 3 4
Thats a couple of recs for places outside of tokyo, inside tokyo i would just add to what others have said by saying; try to find an all you can drink kareoke, they are brilliant fun

Also, in Ikebukuro there is 60 story building, i think it's called sunshine city, go to the 60th floor and you will have a brilliant view of the sheer scale of tokyo and if it's a clear day you will even be able to see Mt Fuji (
Pic)
A few more places to add to your list
EDIT: About the whole question thing. Dont let age dictate when you do it, just make sure you feel like it's the right time when you do, make sure that you can see a long future ahead of you etc. Doing it while away on holiday also has it's risks, if she was for some reason to say no while you were away that would screw up the rest of the holiday, but on the other hand it could be the most memorable moment in your life. Make sure you are sure and ultimatly you are the one who has to decide, not an internet forum.