Well, if I only had 7 days and I was on a budget, I would probably leave out Hokkaido. I believe that the cheapest possible air fares are around 20,000 yen round trip, plus the flights add another layer of complexity to your travel. I would think long and hard about what I wanted to do in Hokkaido and whether it would be worth the tradeoff. There is so much to do in and around Tokyo! I don't know where you're from, but from a U.S. perspective, adding Hokkaido on to Tokyo is sort of like adding Oregon to a vacation in San Francisco. Hokkaido takes time to get to, and it is HUGE.
Personally, rather than spending 20,000 yen or more on a flight to Hokkaido I would be inclined to spend the money on a somewhat better hotel, rather than going with the "most budget" accommodations. Spread out over seven nights, it means you could spend close to 3000 yen more per night on lodging, which can make a lot of difference when you're in the budget price range. Or spend some of that money on transit for a couple of interesting day trips such as Nikko or Kamakura. (A JR Pass is generally not a good buy unless you are making a couple of pretty long trips, like a round-trip to Kyoto, by the way.)
For accommodations, unless you are really on a shoestring I would probably look at business hotels (in the 6000 to 9000 yen per night range for a single; around 8000 to 12000 for a twin). This is where 3000 yen per night can make a huge difference. For example, Toyoko Inn, towards the lower end of the range, doesn't let you go back to the room during the daytime, but Hotel Villa Fontaine, on the upper end, lets you come and go as you please throughout the day, plus the rooms are a little classier.
You might be able to find a place that gives you a weekly rate, or a Japanese style hotel where you can put 3 or 4 people in a room to save money, although these places are harder to find.
As for planning your own trip, I recommend that. You have to be willing to put a lot of time into it, but having done your homework you will enjoy the results better than being spoon-fed some packaged tour that costs way more than you would spend on your own. If you're too busy to plan, though, a tour package is probably better than just showing up in Japan without a clue as to what to do next!
Booking hotels can be overwhelming if you've never been to Japan and don't speak/read Japanese. I recommend Rakuten Travel, Toyoko Inn (although their English web site doesn't always work very well) and Hotel Villa Fontaine. Or spend a lot of time reading posts on this forum, and take notes. (Some of the best deals are available through individual hotels.)
For flights (especially if you decide to go to Hokkaido or if you decide to buy a rail pass), you might want to contact a Japanese travel agency that has branches in your country (such as JTB or IACE does in the U.S.)
Whatever you do, have a splendid time!
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