American student looking for cheap apartment.

Maybe you could place a add yourself?
You could screen people and decide who would fit your lifestyle etc. as a room mate.
Possibly if you can afford it, maybe rent a flat yourself and then find your own room mates since there seems to be a need for rooms?
It could be possible your school has a community billboard where you can place a add for either a room for yourself or for roomies in your own rented flat.
You have to find a landlord willing to have several students living in their place though, not everyone wants to have students coming and going in the house.
Some buildings do not allow for short term rentals so you may have to sign a long term lease.

Rents are going up in the city so you will have to have at least 2 other roomies to cover the rent and other household bills if you want to stay in the $250. a month range.
Doesn't your college have a "student services" office that can help out finding a place to stay?
We had 2 HU college aged students living above us a few years back,
they ruined it for any other college students in our building.
They moved in God knows how many people under the table and held after hours parties at least 2 x a month, started by waking up the entire house at 2 am and going on until 10 or 11 am.
After a few of those Animal House parties everyone called the cops on them, finally they were thrown out by the flat owner and the place sat empty for years, They trashed the entire apt. so badly the owner just closed the door and couldn't face fixing it to sell for the longest time.
Horror  stories like that make it harder for students to find apts.
I know I wouldn't rent to students unless I intended to never live in my apt. again, gut it after they moved out to sell.
Good luck though I am sure some owners own several apts. and want to see income every month and don't intend on living there themselves ever again.
We once rented in the 5th district for just 6 weeks in the summer before we moved to stay in Hungary. The owner only rented to students during the school years and we just happened to need a flat between school times.
It was dirty as heck with nasty used beer bottles stacked up in boxes, not sure why the owner didn't bother cleaning up before letting to us but we worked it out in rent costs because my husband spoke Hungarian and told her that we were not too happy about being her janitor.
If you know anyone who speaks Hungarian they can look at local papers that usually do not advertize in English.

My American born dual citizen son rented a room for 2 months in Sweden when he was 21 years old.
His first time away from home, he was there for a 2 month long visit.
Stayed in a hostel for a few days but searched the papers for a room to rent for the 2 months time.
This was about 20 years back now.
He found a add placed by a older US guy from FL. who had a room to rent out.It all seemed too good to be true, low rent and ready to go.
My son moved in and all was good for a few days time.
The guy said out of the blue that his grandmother was ill in the US and he had to go see her right away.
He left my son alone in the flat and took off.
Well within a day or two several people were pounding away at the door. Most were Arab guys looking for blood, seriously.
They put their hands through the mail slot and said they were going to murder my son!
Unbeknown to him, the guy who rented out the room was a scammer who ran away and left my son holding the bag!
It seems he had collected some fees from other renters in advance and left town with their money, leaving my son as the fall guy without a clue as to what was going on.
He was terrified for his health and safety.
He went to the police station in Sweden and they basically just laughed their heads off.
My son met a couple of young Swedes and told them what was going on, they said no problem they would move into the place for free and protect him from any danger.
He let them move in but he took off for a hostel again, lost first and last rent money just like those Arab guys had lost.
Just saying be careful who you deal with, might be a good idea to use a legit rental agent.