Welcome to Westport Apartments. Our one, two and three-bedroom apartments in Angleton, TX, offer a modern feel with a touch of character. Our apartments, like our residents, are unique. Find cozy interiors with time- tested design touches paired with carefully crafted exteriors. Your new apartment includes a light-filled living space, dishwasher, and refrigerator, so you’ll feel at home right away and be able to keep up with chores easily.