Ashley Greene is looking to move downtown. The “Twilight” star has been telling pals she “will keep her place in LA but wants to spend more time in New York with a view to making a permanent move. She is looking at one-bedroom apartments to rent and plans to bring her dog.” Greene was spotted checking out Port 10 at West 28th Street near the High Line, and Atlantic Development’s 2 Cooper Square, where apartments rent for up to $20,000 per month and come with a rooftop pool. A rep for Greene told us, “Ashley plans to be bicoastal.”