if you haven't already gone, i might have some advice.
first, if you're flying into Narita, I would get a JR Rail Pass before you even leave for Japan. i don't think they're available in-country, so it's a pre-trip decision..
I bought a 14-day rail pass last Spring, and I found it well worth the initial cost. the rail pass price might seem steep when you're already spending a lot for airfare, but i would recommend checking it out.
basically, you buy the pass before you leave, they mail you a voucher, you take that voucher to japan and activate it at any train station. then, for the length of the pass you can hop on and off trains without constantly buying tickets. the more you use the trains the more of a deal it will be.
some stations can get crazy busy and hectic, so its nice to just show the pass at the ticket office and they wave you through without much or any conversation needed.
also, if you're trying to avoid the expensive spots, having the Rail Pass makes it easy to hop on participating Shinkansen trains for a fast getaway from the pricey cities.
i would recommend taking the Shinkasen south as far as Hiroshima, get out there and take the local JR train south to Miyajima Island. There is a nice, inexpensive hostel right by the boat station in Miyajima and plenty to do in area. Miyajima Island is nice to explore and Hiroshima is close enough with plenty to see and do.
Also, there is a military base a little farther south from Miyajima, not that you can or need to go there, but i know from experience that there are always American military folks in that general area, so if you need help translating or asking directions, they might be able to point you in the right direction. just a friendly safety net.
Then, work your way back north to Tokyo, stopping wherever you feel like.
Osaka is a nice, big city alternative to Tokyo and probably not as pricey as Tokyo if you play it right.
Kyoto is also along the way. I love Kyoto, lots of old historical sites and still plenty of modern Japan to explore. Plus, there is a pretty good backpackers hostel in the heart of Kyoto.
Then, finish up in Tokyo and spend up the rest of your vacation budget there. It can be easy to spend all your money in a very short amount of time in Tokyo, simply because there are infinite things to do there.
However, it is possible to do a budget trip to Japan and not go home bankrupt and STILL manage to have seen a lot.
As for time of the year, it all depends on your personal interest. Japan is a pretty long country with sub-arctic northern areas like Hokkaido and sub-tropical areas like Okinawa. Winters are cold, Summers are hot. Spring can be very nice if you catch the Sakura blooming. Make sure to check if its Typhoon season, because you might end up spending all your time in the rain.
hope some of that helps.
