Medina County Apartments For Rent . Explore 28 apartments for rent in medina county with rental rates ranging from $615 to $3,086, giving you a great selection of apartments to choose from. Just use the filtering options available to find properties. 103 Bar Harbor Blvd, Medina, OH 44256 Trulia from www.trulia.com We found 17 apartments for rent in medina county, tx. 780 violet ave, medina county, oh 44321. The median medina county, tx rent is $990 which is below the national median rent of $1,469.