I want to begin with the fact that I went to Sophia University (上智大学, Jōchi daigaku)for a year.
Choosing a school:
With Sophia it was a good school and there is definitely some prestige to the name. In my experience, when I let Japanese people know what school I attended, it was like saying I attended Stanford or Berkeley. The FLA(faculty of the liberal arts) program is all in English. They have an decent selection of classes. Sophia is one of the top schools with the largest English program. FLA students make up about 10% of the entire Sophia school student body. It may have risen since I was there.
Other schools you may want to consider is Temple, ICU, and Waseda. and Keio University. Tokyo University, aka Todai, I believe only has specialty courses and graduate programs in english. All these schools are all in Tokyo area.
Applying and getting into these schools as a degree student is not difficult. The requirements for a foreigner are not NEARLY as strict as they are for Japanese.
Things you should know before choosing a school in Tokyo:
Tokyo people are notorious for being a little distant, so you may not be able to make as many super japanese friends. Instead, you'll meet a lot of quasi-americanized japanese that are friendly, and chill but likely speak a lot of english. I went to Tokyo with determination to make Japanese friends. I joined clubs, and tried really hard(more than I should have really...) I tried to speak completely in Japanese, be more japanese...but in the end...I didn't succeed to the extent I wanted to.(This was a consensus among many of the exchange students)
You will however be able to meet a lot of other students around the world, which was great experience for making multicultural friendships. European, Australian, Taiwanese...you name it... it's all good.^_^ I made a lot of everlasting friendships and I wouldn't trade them for the world.
More Information about My Sophia experience:
Sophia is one stop away from Shinjuku, and is in central tokyo. Extremely convenient location, but if you live out in the sticks, the commute can be rough.
Sophia has contracts with many schools, so you might consider a year long study abroad, instead of signing on as a degree student. That is what I did, My home school is University of San Francisco.
My personal opinions of the Sophia are not that great. I loved the people at th school, but I honestly wasn't that impressed. It could be possible I maybe more accustomed to American style of teaching, thus giving me a biased opinion. I like the more challenging ,"hit the ground running" kind of learning in American schools. School in Japan are by FAR much more laid back than American Universities.
In the end, 1 year was enough for me... it also didn't help that I was paying 17k+ of my schools tuition per semester. (Note: directly applying to Sophia is a much better idea, tuition is significantly cheaper) Even with the direct contract, many of my units couldn't transfer...that could be faulted on my own homeschool though.
I wasn't impressed, however, I met a few people who decided to transfer to Sophia. Their reasoning still evades me, since a Japanese Degree isn't worth diddly in the states. So not only have you squandered your "education", but you are completely ill fit to go beyond office grunt in the American world. Only those with severe ambitions can really take a lot more out of their Japanese experience outside of school. I maybe being a little critical, but I feel that many of the exchange students squander their experience more than cherish it. So I see no point in wasting your time,money, and energy if you aren't bettering yourself or the world with it. Alright..cathartic sequence...over...my apologies...
Anywho... Sophia is one of the better programs you can choose from.
My Personal Suggestions:
If it is more about learning Japanese, I would recommend a place closer to the outskirts like ICU. Where people are more friendly and likely to chat it up with you. If you are severely determined about japanese...skip the program and opt for language school. I attended Naganuma my last 4 months in Tokyo. I learned more in those 4 months thanthe 12 months before.
If you want to pursue your desired major, than your best plan is to go to an American university, and spend some time abroad. Because many of the programs don't have as wide of a selection in your major and an American school would. So be sure to find a school that is contracted, and just try to take your general requirement courses at the Japanese University.(Literature, History, English, that kinda thing) Sophia's FLA website isnt googlable...so be sure to go to http://www.fcc.sophia.ac.jp/index.html . They have a class catalog you can look at also.
Additional options: You can also do the CIEE program to Sophia, but I think it's ridiculously expensive. The benefit are the liaisons, and cultural field trips. In my 15 months in Tokyo I have met many students in CIEE, trust me when I say you would prefer to go outside of the program, and keep your freedom.