Poznań has a big variety of hotels from 5-Stars to 2-Stars and as well some cheaper hostels.
There are a possibility to rent an apartment in a private house.
We give only some suggestions:

2-Stars hotel
Ibis Hotel Situated on the bank of Warta river, quite convenient way to University by tram (about 10 min.)
3-Stars hotels
Hotel Ikar Only 5 min. on foot to University .
Hotel Topaz Situated near to main railway station. About 15 min. on foot to University. Our Institute has booked rooms for guests here since years.
Hotel Rzymski Almost a symbol of hotels in PoznaƄ and with big tradition. Luxurious but more expensive than other 3-stars hotels. Located in the strict center of city. 10 min. on foot to University, or 4 min. by tram.
4-Stars hotel
Nh Hotel Situated very close to university 5 min. on foot.
5-Stars hotel
Sheraton Poznan HotelThe most luxurious and most expensive. 10 min. on foot to University. Only 5-6 min. on foot to main railway station.
Very Berry Hostel. Situated in the heart of city, 10 min. on foot to University.
Frolic Goats Hostel. Located near to Old Market, about 15 min. on foot to University or 5-6 min. by tram.
Hill Hostel. Another hostel situated near to Old Market, very close to tram stop (4-5 min. to University).
It is possible to rent a flat with help of some agencies:
Przemyslaw (page also in English), (this agency has existed since many years and has good reputation)
Delta (rather expensive)
Roletim These offices are acting in Poznań, but some apartments could be situated in varoius city districts. The longer way to the center, the cheaper flat.
During July and August will be open an International Sudent's Hostel, situated only a 5 min. on foot to University.
You can also see Accommodation in Poznań