In general, the closest accommodations outside of Hyde Park (location of the 57th Street Art Fair) are near McCormick Place, in the South Loop (15 minutes away), near Midway Airport (45 minutes away) or in East Chicago, Indiana (15-30 minutes away).
Accommodations in Hyde Park:
Chicago Lake Shore Hotel
4900A S. Lake Shore Drive
Hyatt Place Chicago South/UniversityMedical Center
5225 S. Harper Avenue
La Quinta In & Suites by Wyndham Chicago
4900B S Lake Shore Drive
Sophy Hyde Park
1411 E 53rd Street
...also check out Airbnb for current listings in the Hyde Park area.