Carroll Gardens is an area of Brooklyn bordered to the north by Boerum/Cobble Hill and to the west by Red Hook. The area has long been a working class Italian area but it is being invaded fast by upper middle class brownstone owners and the young people who are renting the buildings from them. There is also a large Latino population in the south end of the neighborhood.
Carroll Gardens is a beautiful suburb but at a lower price than its neighboring areas and represents a good bargain for Brooklyn. Rents here are more affordable than you would find in other areas in this part of Brooklyn but it still has many of the same amenities although it is a bit isolated by the lack of public transport options. Only the F and G trains stop here at Smith Street and 9th Street and if you find yourself moving to Carroll Gardens, you might find yourself needing to walk a bit to gain access to public transportation.
Living in Carroll Gardens means that you won't have access to a close, large supermarket. Fortunately it makes up for this with the numerous smaller, local shopping and eating choices. On Smith Street, Zaytoons has cheap BYOB Middle Eastern fare and Cafe Cubana makes a mean mojito and serves up excellent Cuban food. Carroll Gardens is home to a sizeable French population and Smith Street is also home to three French restaurants. Lucali on the corner of Henry and Carroll Streets is known to make one of the best pizzas in New York. South Brooklyn Pizza is another good place but is probably more well known for the recently launched gay bar/dance party on Monday nights. There are also plenty of small shops to suit most of your needs including Mazzola's Bakery on Union Street and G. Esposito and Sons, a meat market famous for their fresh cuts.
During the summer months the Gowanus Yacht Club has outdoor picnic tables and serves pictures of beer and hotdogs. PJ Hanley's on Court Street and 4th Place is another good place to enjoy a beer outdoors and they have live music on Wednesday nights in the summer. If you would rather avoid the bars then Carroll Park is an area of playgrounds and sitting areas. Prospect Park is a 30-minute walk away if you would prefer a larger outdoor area to kick a ball around or suntan.
Overall Carroll Gardens makes a great choice for new arrivals to New York City. It is a safe area with lots of amenities and it isn't too far from lower Manhattan. It has a nice atmosphere and would make any newcomer feel welcome to what can otherwise be a very intimidating city.