Sunset doesn't have neighborhoods -- it is a neighborhood. The area caters to families, so finding 2 bedroom apartments for rent is no problem. If you want complete luxury, you can find all-utilities paid condominiums in quiet communities close to the beach. However, a lot of these don’t allow pets, so you may find yourself choosing between the plush life and the plush dog.
This town is packed with a variety of choices in apartment complexes and apartment homes. The rent ranges from high priced homes to less expensive apartments, but anything here will be more affordable than beachside communities or Miami itself. It is not hard to find what you want, because, as a tourist hot-spot, properties abound, and they cater to a huge range of potential renters. $$
If you live in Sunset, you're most likely a fan of sunshine, the outdoors, and water sports. People here take advantage of the beaches and waves in Miami -- they surf, lounge in the sun, waterski, and are generally active people. There is a huge multicultural population in the area; it's welcoming to people of every nationality. So come here to meet a diverse community and soak up the culture (if you speak Spanish already or are looking to pick it up, this is a great choice!), and, of course, to soak up the sun.