Apartments For Rent New Canaan Ct Craigslist . The average apartment rent in new canaan costs $2,487. The average rent in new canaan is currently $4,500, with apartments ranging. 109R Rosebrook Rd, New Canaan, CT 06840 Trulia from www.trulia.com Fairfield county (subregion of nyc site) Short term rental 3 bed 2 bath 2500 sqft. If you're apartment hunting in new canaan, here's what to expect: