Apartments For Rent In Riverside Avondale Jacksonville Fl . The median riverside, jacksonville, fl rent is $1,500 which is above the national median rent of $1,469. Avondale 1st floor apartment for rent. 3637 Oak St, Jacksonville, FL 8 Bed, 4 Bath MultiFamily Home 4 from www.trulia.com Avondale 1st floor apartment for rent. This apartment allows cats and has parking. 2913 post street, jacksonville, fl 32205.