Augusta Maine Cheap Apartments For Rent And Pet Friendly . Apartment rent in augusta has increased by 2.7% in the past year. See all 9 pet friendly houses in augusta, me currently available for rent. 15 Floyd St, Brewer, ME 04412 3 Bedroom House for Rent for 1,400/month from www.zumper.com 340 granite hill rd, manchester, me 04351. Try rentals.com to compare amenities, photos, & prices to find houses that match your needs. Augusta pet friendly apartments under $900;