Rincon Apartements is now called Avistele at River Oaks. The Memorial Heights area of Houston borders the presitigious River Oaks neighborhood and offers luxury apartments for lease such as Rincon and Avistele at River Oaks. Oversized closets and granite countertops at Rincon Apartments. These privately owned Rincon apartments called Avistele at River Oaks is located in the heart of Memorial Heights in River Oaks Houston and provide easy access to major employers, shopping, dining, nightlife and everyday needs.