Apartments For Rent New Canaan Ct . Browse all the houses, apartments and condos for rent in new canaan. The average home rent in new canaan is $7,765. 143 Heritage Hill Rd New Canaan, CT, 06840 Apartments for Rent Zillow from www.zillow.com New canaan features 101 low income apartments with rental assistance where households typically pay no more than 30% of their income towards rent. 95 richmond hill rd #a, new canaan, ct 06840. The median new canaan, ct rent is $6,900 which is above the national median rent of $1,469.