Oak Grove for Rent in South Austin, Texas. Oak Grove Apartments is a small, friendly, affordable apartment complex on a little under four acres in South Austin, Texas. The property was developed in 1979 and includes ten two-story brown-shingle residential buildings in a hilly, multi-level wooded setting. The complex features 1- and 2-bedroom floor plans, some with fireplaces and vaulted ceilings. Oak Grove is located near the intersection of Highway 290/71 West and South Alpine Street. Sandwiched between the popular South Congress and South Lamar areas, you’re within walking and bus rides to thriving and eclectic music, shopping and dining districts. And you’re just minutes away from Austin-Bergstrom International Airport, museums and the University of Texas.