Looking for a cheap apartment for rent in Potter County, TX? With RENTCafé, finding an affordable apartment in Potter County, TX has never been easier. We feature 11 low-priced rentals directly from property managers, with rents lower than the Potter County, TX average. What is a cheap rent in Potter County, TX? The average apartment rent in Potter County is $681 per month so any rental south of $545 would be considered cheap here. Size matters though, so if you are in a market for a studio, expect to pay around $379 per month. If you’re looking to upgrade to a 1-bedroom apartment you’ll pay around $423, while a cheap 2-bedroom apartment will cost you about $519 per month.