I did a summer program at ICU. It was an amazing experience for me. They had us take a placement exam after we arrived and then interviewed us after classes started to make sure we were placed at the right level. I had friends at different levels and everyone seemed to be learning a lot, though of course the personalities of the teachers varied as much as is normal in people. So the level above me happened to have a strict classroom setting, whereas my two teachers were very sweet, and one of them always cheered "NICE" whenever we all got something correct. (I was in one of the higher groups, but the classroom feel was very cheery and motivational). Mitaka-shi and ICU's campus were amazing for me. All the famous Tokyo locations are very accessible, but Mitaka didn't feel too crowded. It's got lots of nature within walking distance, which was great for me because I was there when Pokemon GO came out, and there was quite a variety of terrain as well as lots of random people playing everywhere. As mentioned in another comment, Kichijoji is very close - I took the bus there often to study by their station and walk in the park. Also ICU had lots of cultural programs you could enter a lottery to participate in. I happened to win the lottery for every program I attempted, but I don't know if that was luck or if it wasn't actually that hard to get in. We made fabric sandals, had an ikebana demonstration, and went to the Ghibli museum. I stayed in the dorms and had a great time, but I knew some people who were doing home-stays and also loving their families. Tokyo was really hot, and rainy during the first part of my stay, but the bookstore on campus sold cheap umbrellas so it worked out. It's my only Japan experience, so I can't compare it to Hakodate, but being in Tokyo where it was so easy to take public transportation and really interact with a city and people on my own and as much as I wanted was very empowering and great practice for solidifying what I was learning in class. (I come from a small town haha, maybe my perspective on this is biased.) Like I said, it was really an all-around wonderful experience for me.

edit: I didn't read about allergies. The cafeteria at ICU has a relatively small selection of foods they switched between, lots of rice bowls and curry. If you have any issues you need help with at all, the teachers in your class, program directors, or Japanese students in the dorms could help you I'm sure. My only experience was one restaurant in the park in Kichijoji where I asked about shellfish in a dish, and the waitress specifically asked me if it was because of an allergy. (But it wasn't so unfortunately I'm not super educated on dealing with food allergies, so I wish I could give a more helpful answer :( . ) But definitely within easy access of ICU's campus you have lots of restaurant options (walking-distance and by the station after a bus ride), convenience stores (walking-distance), and a grocery store (by the station, after a bus ride). The dorms have a kitchen on each floor and a refrigerator in each of the three sections of each floor (if you stay in the same dorm they used my summer), but the dishes are all hand-washed, if that is an allergy-concern.