Fort Myers Apartment For Rent Close To Hospital . Find your next apartment in fort myers fl on zillow. Rent.com has 65 apartments available now. The Edge Apartments Fort Myers, FL from www.abodo.com Looking for townhouses for rent close to park royal hospital, fort myers, fl? As of june 2022, the average apartment rent in fort myers, fl is $1,425 for a studio, $1,788 for one bedroom, $2,175 for two bedrooms, and $2,004 for three bedrooms. Freshly cleaned and ready for new residents.