Well, you certainly don't fit my age demographic by a couple of years but you certainly do fit my travel style.

For eleven days, I think 3 days Tokyo + 2 days (1 night) Hiroshima/Miyajima + 4 days Kyoto/Nara/Kansai + 2 travel/airport days sounds about right. If you plan on getting a Japan Rail Pass - and you should for that much train travel - it would probably break down as:

arrive NRT - overnight Tokyo
start Rail Pass
to Hiroshima + half day visit
overnight
Hiroshima/Miyajima + travel to Kyoto
4 days Kyoto/Nara/Himeji/whatever
to Tokyo
end Rail Pass validity (7 days)
Tokyo 3 days
Depart NRT for home.

Just plan to do your major travel during the time period that the Rail Pass is valid. A mistake here could be rather expensive.

The "hot springs" would probably come out of the Kyoto stay or perhaps during the travel day back to Tokyo. I will defer to others regarding this as I stay out of them. Much prefer the deep Japanese baths at the hotels.

As for "can't miss" places, that is very subjective. You will probably be a bit early for the cherry blossoms unless we get a very early spring. Pray for unseasonably warm early spring. You might get lucky and get a few hana during the last few days of your visit. If so, plan on visiting one of the big parks in Tokyo (or whichever city is your last stop.) I like the sakura display at Hama Rikyu Detached Imperial Garden but any large park, temple or garden will be nice.

In Hiroshima, plan enough time to visit nearby Miyajima Island. There is a ferry from the Hiroshima dock which you can pay for with a JR Pass. That is worth most of a day, which is why I suggested an overnight.

Himeji is a nice half-day visit which can be done on the way back east from Hiroshima or as a day trip from Kyoto. In addition to the famous castle, Himeji is a bit smaller and less frenetic than Tokyo/Osaka/Kyoto. There is an interesting shopping arcade one block over from the main street which is the route to the castle from the station. Just walk it and return through the arcade rather than back on the street. If you are looking for lunch on the way to or from the castle, there is a very good tonkatsu/katsudon place about half-way on the right facing the castle.

For Kyoto, just look through your guidebooks and pick out some spots that look interesting and plan out a skeleton itinerary. There is too much to see in such a limited time so you will have to pick and choose. I recommend Nijo Castle, Sanjsangendo Hall, the Heian Jingu shrine, Gion along the river at dusk, at least one big temple - Nishi Honganji, Kiyumizudera, Nazenji or any of a dozen others -, Kinkakuji (the golden pavillion) or Ginkakuji (the silver pavillion) or both if you have time, perhaps Ryoanji for the rock garden and beautiful park and lake, an evening walk along Pontocho alley. The Imperial Palace park and garden makes a nice spot for a picnic lunch. The Palace tour itself is strictly optional. I don't think it is worth using part of your limited time unless you just really want to see it.

If time allows, you might take the train out to Arashiyama. Start your walking tour near the monkey preserve in case the snow monkeys don't work out. Arashiyama is outside of Kyoto proper and is much more rural and rustic but has some nice sights.

Depending on time and inclination, there are several daytrips from Kyoto - you might even wish to add a day there and cut someplace else. You could take short train rides to Himeji, Nara (most of a day,) Osaka, Lake Biwa or into the surrounding hills for that onsen visit. Use that JR Pass! Get your money's worth.

Tokyo is much more dependant on your tastes. I recommend a mix of the traditional - a visit to Sensoji and Asakusa or Yanaka/Nezu/Ueno, the Hama Rikyu garden - and the ultra-modern -Ginza, Akihabara, Shinjuku or Harajuku. If you want a museum, I recommend the Edo-Tokyo Museum which has the advantage of being next door to the sumo museum - a two-fer.

Hotels may be a problem on such short notice. You don't mention budget or style preferences but for a college student, you may wish to look at hostels or "business" hotels, which range from pretty basic to quite nice. If you will let us know what you might be looking for, I'm sure we can help find some resources. Lap Lap seems to have a whole list of recommendations for all price ranges. Do start looking for hotels right away as time IS running out. For such short lead-time, you will need to jump on the Rail Pass issue also, unless you are in a large city with an authorized seller at a local travel agency where you can just walk in.

I applaud your desire to just catch dinner at someplace near the hotels. Look in the small side streets for local places for great food at good prices. To save money, consider making the midday meal your large meal of the day. You can often find the same food that will be on the dinner menu for half the price at lunch. I like to scout the places that the locals use for lunch - look for crowds - and then come back after 1:00 pm to miss the lunch crowds. Plan to try some of the standard fare - ramen (have to have Japanese ramen,) udon or soba, tempura, curry rice, some sort of donburi (I really like katsudon) and several others. Look at the plastic or photo food displays and just try whatever looks good or interesting. It is all good. Try some street stall food at the temples. Around Sensoji in Tokyo, you can find almost anything. It will be safe, cheap, fresh and hot. I dare you to try takoyaki. If all else fails, the fresh choices available at convenience stores is 1000x better that what you get here and you can find *Bux and McD's everywhere (yuck.)

Whew! Firm up some ideas and preferences and we can probably give you some specific ideas.

JR