Here's a map of my plans of action if I were you (hopefully ti would help)
1. Get a Youth Hostel Membership Card- it's 35$ and you save on average 5$ a night so it's worth it. You also get a free magazine subscription and good guides on traveling. And it's good for a year, so if you ever go anywhere again...
2. Find a cheap flight. Make sure you arent planning to go during any holidays or it's the high season or you'll be paying for it. Wikipedia will show you the best times to go. Test the days of the week you fly out and in on, cause that could change prices.
3. Get a rail pass. Buy it online and get it mailed to you. You can't buy them in Japan, but like Hatix said you get a voucher which you use in Narita airport in the JR place. The person I sat next to on the plane was so helpful and took me there
Get it stmped so you can use it right away, cause you can use it to get into Tokyo for free. Decide how much travelling you will do, and then what rail pass you'll need. If you just go to Kyoto and back it will already have paid for itself right there.
4. Find a hostel for the dates you will be there. Book the first few days. It probably says it's all booked because you are looking so many months in advance! I recommend Tokyo Yoyogi youth hostel. You and your girlfriend will be in separate roms, but you get individual rooms and it's 30$ a night and they are very helpful. It's right by shinjuku so it's central and easy to get to. I think I've talked about that hostel in here and it's the same on the creator of this thread sayed at. The best part about it is it has this awesome breakfast buffet next door that all the school kids and other travellers use and it's sooooo yumm- all you can eat and drink for 4$.
5. Plan your itinerary and have fun! Japan in incredibly convenient but you should still have a rough idea of what you want to do when. Searchthe internet and read some travel books on Tokyo and Japan- make a list of what you want to see