Renting an apartment in Tokyo for 10 months

Hello everyone,
I have applied to go on an exchange year to a University in Tokyo in correlation with my University's exchange program. I will be coming to Japan approximately September 2018 until August 2019, so I will be staying in Japan for about 10/11 months. I'm having a lot of problems finding suitable and reasonable accommodation. I would like to rent privately (no share-house, home-stay/host family) and will be renting together with my boyfriend, who's Japanese and already living in Japan.
We're both really confused and lost, we don't know where to start to look. I was wondering if there are any websites/agencies/rental agencies (in English or Japanese is fine) that offer cheap apartments for a period of 10/11 months?
As previously stated, we both have no idea where to start looking, and whenever we do, we find apartments that are way too much for two University students to afford, or way too far out from the city.
Any information would be appreciated!

Have either of you asked your university for help? Many universities have housing departments that not only handle university residences but also have information about off campus private rentals as well.

My university only offers information on university dorms/share houses, which we wouldn't be able to rent together to start with, according to them.

The harsh reality is that you are not going to get favours just because you are university students. You are competing for property just like everyone else so do not expect a discount price close to where your school is.
If you want cheap, pick something small, old and unpleasant. If you want something livable (and cheap), go further out.
Have you checked UR apartments? I know some people paying 60,000/m for something reasonable over in Saitama (too far you would say). I pay a bit more, but I have all my utilities included so it works out pretty well for me.
And while I might live far from the centre of the city, I don't have to commute every day (40 minutes to Shinjuku or 60 minutes to Tokyo - it's not so bad).

You are both
- Unmarried (unmarried couples are tend to be avoided as the risk they suddenly break up and go out is higher than married couples)
- Foreigners (most of the landlords want to rent their properties to Japanese nationals who are familiar with Japanese manners and etiquettes)
- Without steady income
- Without any Japanese guarantor (I guess)
- Who want to rent for a short time (generally a contract for an apartment is for 2 years).

You should compromise.

There is accommodation that is rented out monthly.

Check the following:
setagayachintai.com
tokyoapartments.jp
tokyoMonthly21

Obviously your idea of cheap might not be my idea.... but as it gets closer to The Rugby World Cup 2019 and Olympic Games 2020 there are more short term rentals becoming available.( and being snapped up!) There is another site VRBO Japan that has vacation rentals available, you might be able to do a deal with one of the owners for a 10 month stay.

Sorry an error in the web address:
Setagaya-Chintai.com

Have you checked out LeoPalace 21 ?. They have apartments especially for foreigners, with monthly contracts. I'm surprised your Japanese boyfriend doesn't have any ideas. If you need a guarantor (and in some cases they are not necessary) maybe his family could help out.

I rent through OakHouse (I met the owner one night - odd story), and they have a mix of properties around the city. Some nice, others not so great. What is acceptable depends on your particular preferences.
When apartment hunting (which I have done a couple of times) I did notice that some of the companies target foriegn workers that are on expense/relocation packages and those prices are probably double what they need to be (i.e. 200,000 yen/month for something a normal company would offer for 100,000 yen given the area.)
A related comment on UR (my staff rent with them), they do shorter term contracts and you can also pay a year in advance - they have a pay 11 months, stay 12 deal.