Cheap Apartments For Rent Costa Mesa . 5 rows 931 w 19th st. The average apartment rent in. 207 Albert Place Costa Mesa, CA apartments for rent from www.apartmentlist.com On average rent for a studio apartment in downtown costa mesa is $2,025, and has a range from $1,666 to. 1 & 2 bedrooms apartments homes, big patios, new renovated units,. Padmapper has 79 condos, houses, and apartments for rent in costa mesa.