The University of Manchester has this page with special discounts at two hotels.

Other options in walking distance include the Maldron Hotel, the Premier Inn on Princess Street or the Holiday Inn on Oxford Road.

There are many options, but those three are probably the most convenient after the Hyatt.

If somewhere near Piccadilly station is convenient, there are the following options:

Manchester Piccadilly Hotel
DoubleTree by Hilton
Native Manchester
Holiday Inn City Centre
Malmaison
ABode

The Summer School does not endorse any of these accommodations. Manchester is a big city and there are plenty of offers available.