Currently, you have 67 options within a five mile radius of Belmont's campus. The campus is centered to the city relatively well; so, you'll have options but not all are 3 BR/2 BA. First let me give you the numbers of ALL the properties.
17 single family homes are available at that price. The remainder are condos. On single home side, you have options in Area 3 near Charlotte and in Area 2 in the Music Row/Edgehill area. The condos include local favorites like BeechTree, The Park at Melrose and several Villager properties.
Geographically, your options closest to Belmont are (1) a condo at the Albemarle which is ALMOST ON campus with 500 sq ft; (2) a three bedroom single family home in Edgehill a short biking distance; and (3) two condos at The Villager in Hillsboro Village.
If you must have a three bedroom/two bath residence, no condos meet the requirements, however eight homes do. Two of them currently are under contract; so, that leaves six options. One is near the Fairgrounds, one is near Music Row and the other four are in the area off of Charlotte.
The good news is you have options at your price point. It's just a matter of what you are willing to give-on to get the perfect place for you.