We recommend staying in either Portland, South Portland (by the airport or mall), Westbrook or Scarborough. Everything is close by!
Also you can check out airbnb.com in these areas.
Hotel
Portland Regency Hotel & Spa
20 Milk Street Portland, ME 04101 (207) 774-4200
Hotel
Tru by Hilton Portland Airport Area
369 Maine Mall Road South Portland, ME 04106 (207) 221-3131
Hotel
Inn at St John
939 Congress Street Portland, ME 04102 (207) 773-6481
Hotel
The Inn on Carleton
46 Carleton Street Portland, ME 04102 (207) 775-1910