Start with your state flagship. But any directionals should be ok - C Ct, Southern Maine, SUNYs - like Buffalo. UNH, Delaware and URI are three more that can work. E Carolina has dedicated transfer housing.
In the Midwest/South (really MW but people see as south), W Michigan, Louisville, Kentucky and for more chill Marshall should work.
For privates, look at Ithaca, Quinnipiac, and Elon might be three a bit smaller but not too small to look at.
Not sure about Greek life but get involved with clubs.
I googled transfer housing on each and all appear to offer or require it.
Good luck.