Hi, ruby and welcome to Massachusetts.
I spent the bulk of my life on the Southcoast so I think I can help a bit (have also lived in Maryland, Maine, and now Boston).
The Southcoast is a nice area. It's on the ocean (beautiful beaches and rivers) and it's within an hour of Boston, minutes from Cape Cod and about 3.5 hours to New York City.
Given what you're looking for in an area, the BEST fit would be Providence, Rhode Island. It's unfortunate that you say you HAVE to live in Massachusetts (any way to change this?) because Providence is about 25-30 minutes from Dartmouth and will offer you the best urban amenities. It's a metropolitan area of about 1.6 million and has all sorts of culture, arts, nightlife, great restaurants, etc. It's also on the local Boston commuter rail trains (MBTA to Boston's South Station in an hour) as well as Amtrak's high-speed Acela Express which services Boston, New York City (under 3 hours), Philadelphia and Washington D.C. Providence has many ethnic neighborhoods (their little Italy, "Federal Hill" is phenominal) and some great institutions (Brown, Rhode Island School of Design, Johnson and Wales, etc). If there is any way for you to be able to live there and commute, it would probably be the best bet for you.
Fall River and New Bedford are often terribly regarded in Massachusetts. I can see many reasons why, but I tend to think the criticism is overblown. Fall River has some nice, suburban-esque neighborhoods (the "Highlands"... along Highland Avenue are beautiful. Loaded with tree-lined streets and old industrial era estates). It also has a cool waterfront area with the world's largest collection of Naval War Ships (which you can board and explore). It has a large Portuguese population and there are some really interesting markets and restaurants in town. It's not very walkable and there are some isolated areas that I would avoid in Fall River.
I would recommend New Bedford before I recommend Fall River. New Bedford is slightly larger (right around 100,000 people) and is a more active seaport. The downtown area is gorgeous (it's a
national park) and very walkable. The streets are cobblestone and there are a good number of restaurants, bars, galleries, and some nice museums (the
whaling museum,
art museum, and
ocean explorium are all very cool). It also has a wonderful theater (the
Zeiterion) and a great
symphony orchestra. New Bedford is really the Southcoast's cultural hub. It's also loaded with history as it's where Herman Melville lived when he wrote Moby Dick about his experiences on a whaling ship and it's also where Fredrick Douglas found freedom (and a big underground railroad stop). Like Fall River, there is a large Portuguese population and many great Portuguese restaurants (mostly scattered throughout the city, not concentrated downtown). New Bedford also has a wonderful little
Zoo set in the Fredrick Law Olmstead (same guy who did NYC's Central Park) designed Buttonwood Park.
New Bedford has some great attributes but it's struggling economically. It's the nation's highest grossing fishing port, but when manufacturing left, many were left without jobs. You can see some urban decay in areas outside the city's core. Like Fall River, the crime is really isolated to certain locations. If I were you and were looking for a home in New Bedford, I would look Downtown, the Whaling District, The West End and along the County Street historic area (many wonderful old homes here).
Crime isn't an issue in these cities save for certain spots (usually around public housing projects) that tend to garner most of the attention. The worst thing about these cities are the lack of jobs requiring a college degree (there's a large uneducated population you'll likely notice), and the poor public education services. If you don't have a family (or are going to put your kids in private schools), Fall River and New Bedford can provide EXCELLENT value for you.
As I mentioned, if you were going to look into those cities, I would highly recommend New Bedford over Fall River. The core of New Bedford is entertaining (though small) and walkable. You're still within a half hour from Providence and an hour from Boston for your real urban needs. New Bedford offers great scale and some stunning architecture. If you're single or not worried about public schools, you will likely find the Downtown/historic district area and the West End/ County Street historic area quite charming and fun. If you do need public schools, you would be better suited outside of the city.
If you look into New Bedford (or Fall River) and find that it doesn't suit you well, then there are plenty of other alternatives. Fairhaven as has been mentioned is quite lovely. it sits directly across the harbor from New Bedford so you can access everything in downtown New Bedford from Fairhaven within about 5 minutes (across the Pope's Island Bridge). Fairhaven has some of the most affordable Ocean Front property you'll find in Southern New England and the center of Fairhaven has an excellent small-town vibe. Their high school is perhaps the most beautiful in the area (the old Durfee High in Fall River is a gorgeous one as well). Fairhaven schools are fairly decent if that's important to you.
Dartmouth itself isn't bad (great public schools). The town takes up a large chunk of land so the neighborhoods are pretty diverse. Closest to the New Bedford line it's almost urban, while in areas like Russel's Mills it's mostly rural. Of course, you do have the suburban areas as well. The coastline in Dartmouth is wonderful. Westport is charming (a lot like rural Dartmouth) but has terrible public schools. The river and beaches in Westport are some of the prettiest you'll find anywhere (I spent my summers in college lifguarding down there); the Boston Globe recently featured a spotlight on Westport
here and a nice photo tour
here. If you want a cool area to start living, see if you can find something in Westport Point, it's a gorgous little peninsula that juts out into Westport Harbor.
Lakeville is very suburban but has some gorgeous lakes (hence the town's name). It has very good public schools and the real kicker is that it has a commuter rail station with service to Boston's South Station. Lakeville is on Route 140 which gives it relatively easy access to Dartmouth, New Bedford, etc. Freetown may also be another good alternative. It's situated conveniently on Route 24 and 140 so you have easy access to Dartmouth, New Bedford, Boston and I-195 (to Providence). I'd suggest looking at the Assonet section of Freetown as it has a nice historic village with a meandering river. It's also right on Route 24 (exits 9 and 10) so you're 20 minutes from Dartmouth, 25 from Providence and 50 from Boston.
Towns like Marion, Mattapoisett, Wareham, Rochester, etc are all wonderful, but you're getting further and further away from having easy access to the larger cities in the region (though you're still within range of Dartmouth).
Craigslist (check the Southcoast section) is the best site for rentals in the area. They've got a good Providence section too if you can finagle that. Rent.com and other sites are good for managment companies, but most people use craigslist.
The Lofts at Wamsutta is a cool apartment complex (brand new) built in a converted mill building. It's close enough to downtown New Bedford and only about 15 minutes from UMass Dartmouth. I'd give it a look.
Anyway, good luck! I hope you find some place that fits your needs.
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Where to live near/around North Dartmouth?
Westport, Lakeville or Freetown
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