30 days $3000 budget trip suggestion

Hi, I'm traveling to Japan from Sept. to Oct. for the first time and I would like some suggestions/help on an itinerary for one person.

Arrive and Depart: Narita

My situation: recently bought plain ticket without any planning. Thinking about getting a 21-day JR Pass. The only other thing I've done is book two nights at a hostel in Tokyo (Sumida-ku). My budget for when I'm there is $3000 USD.
Goal: I want to cover a lot of grounds in that 30 days period.
Interests: Food, Onsen, minor activity.
Not much interest in Museum/Temples.

I've read through most of the online and bookstore itinerary that have 14 days or longer but there aren't many 30 day itinerary.

Please see link below for something I drafted up.
http://shorttext.com/h68l59hf4cu

Thanks in advance.

I recommend to continue to read this website's sightseeing guide and other websites and guide books for inspiration on what places you want to see according to your personal interests.

The user ratings in this website's sightseeing guide tell you how other travelers likes the places:
http://www.japan-guide.com/e/e623a.html

And then once you have a "wish list" to put them together into an itinerary.

If you want to see the entire length of Japan, I recommend to consider domestic flights for the initial trip to the north/south and the final trip back to Tokyo from the south/north:
http://www.japan-guide.com/e/e2364.html

I looked at your travel plans and think you made good choices so far. There is SO MUCH to see (and eat) in Japan that it would be hard to cover eveything. I can only go by my own experiences but if I had to pick one island not to go to due to time and money constraints, it would be Shikoku unless you had time to walk the pilgrim route to view the scenery, but you are not too keen on seeing many temples so you may not feel you are missing much.

I have a theme for this year's trip. I am going to all the past and present capitals of Japan and getting a flavor of each. You might want to make plans to incorporate various similar themes-example-see both A-bomb cities. Go to several big sea ports, pottery towns, see several large rivers. See several theme muesuem. I am making a stop in Uji City to see the Tale of Genji museum, for example. There's the Yamato Museum in Kure which is very intersting, too.

Have fun!

Thanks for the feedback so far.

Questions:
Based on the rough plan below, how many days do you think it will take to cover that?
Which locations should I be spending the night in because I haven't figure that out into the plan?
What do you estimate the budget would come out to be for just those so far?
Is the order of my plan correct/efficient?
Are there any oversights in the plan so far?

-----Plan-----
Asahikawa: Daisetsuzan National Park
Asahikawa: Asahidake Onsen
Asahikawa: Asahiyama Zoo
Sappora: Sapporo Beer Museum
Sappora: Susukino in Sappora
Hakodate: Onuma Park (Onuma Koen)
--maybe Noboribetsu: Daiichi Takimotokan
--maybe Noboribetsu: Jigokudani
Tazawako Station: Nyuto Onsen
Nyuto Onsen: Tsurunoyu Onsen
or
Nyuto Onsen: Ganiba Onsen
or
Nyuto Onsen: Taenoyu Onsen
Hiraizumi: Motsuji Temple, Chusonji Temple, Takadachi Giekeido
Nikko: Toshogu Shrine
Tokyo: ---undecided plan
Kamakura: Engakuji Temple, Kenchoji Temple, Hachimangu Shrine, Hasedera Temple
-----End of rough plan so far-----

I'm using the Sightseeing Guide and planning according to region from top to bottom.
(http://www.japan-guide.com/e/e623a.html)

Things to note which might turn into issue: I don't speak any Japanese but I have a phrasebook. I will most likely carry my backpack luggage with me from place to place.

Thanks.

Great resource to use, however some of the time you have left should be spend in actually securing lodging. I find that to be the hardest and most time consuming thing to do before a trip :) Plus with your lack of Japanese language you may have to spend more time on the fly figuring out how to get from one place to the other-unless you spend a good bit of time now to figuring it out. You can always "camp" outin a station if you can't find a hostel on some days, but Japanese Customs want an actual address when you enter.

Staying anywhere near an onsen town is expensive so you might want to find a town nearby to fall back on if you can't find something within your budget.

I think your budget is realistic for a backpacker-although you did say you like to eat :) Cheap food is usually good, but a person can spend a lot more at most restaurants.
Good luck!