Dubuque County Apartments For Rent . View rentals in dubuque county, ia. There are 25 low income housing apartment communities offering 1,146 affordable apartments for rent in dubuque, iowa. 408 S Dubuque St, Iowa City, IA 52240 House for Rent in Iowa City, IA from www.apartments.com View rentals in dubuque county, ia. We found 36 apartments for rent in dubuque county, ia. In addition to the rent cost, you need to also account for costs of basic utilities consisting of water, garbage, electric and natural gas.