There are plenty of decent towns around Fall River to look into. In fact, the real estate in the South Coast is some of the most affordable in Eastern Mass. so you can find a great piece of mind in a small community right nearby the city.
I'll list a few for you, but the list is certainly not limited to these:
For a more rural experience:
Assonet/Freetown- Assonet is a village on the west side of the Town of Freetown. Assonet borders Fall River to the North and is easily accessible via exits 9 and 10 off of route 24. Schools are great (don't know if that's an issue for you) and the recreation facilites are fantastic for future kids (in fact, there is a "mini-fenway" right next to the elementary school for little leaguers). The people are friendly, and it is a comfortably small town (pop. 9,000) close to larger cities (fall river and new bedford). In fact, my parents still live there.
Westport- Westport borders Fall River to the East. It's a community with a diverse geography. In S. Westport, you have some of the most beautiful coastline in New England it's got a state beach as well as a nicer town beach for Wesport residents. In the central areas of town, you have farmland mixed with homes. It borders on suburban and rural with a river running through it. There is a vinyard/winery in town as well as the Buzzards Bay Brewery. in the northern part of town you have a large pond (really a small lake) that is home to many summer vacationers. This pond acts as a border with Fall River.
Tiverton R.I.- Tiverton borders Fall River to the south. The northern part of town is actually pretty urban because of its proximity to the Southern part of Fall River. the rest of the community is VERY quaint and quiet. it stretches along the Sakonnet river and offers a beautiful harbor as well as some nice beaches (Fogland is gorgeous).
Some other towns to look into:
-Dartmouth
-Somerset
-Swansea
-Little Compton, RI
-Berkley
Fall River is sort of a dying mill town. It's not completely dead, and if you like good restaurants, there are some for you. There's a large Portuguese population in the area, and their food is fantastic. There's also a professional culinary arts school in town which operates a few restaurants (I'd check out the Abby Grill if I were you). If you need suggestions, just ask. Nightlife, and performing arts are a different story. The Narrows Center for the Performing arts is quirky and nice, but it's just about all Fall River has to offer. There are a few decent bars, the rest should be avoided (again, ask for suggestions).
The best of the arts and culture are 15 minutes away (straight shot West down I-195) in Providence (or 45 min. away in Boston if you want to drive that far). Providence is a GREAT little city; if you liked Portland, ME, you'll LOVE Providence. New bedford, 10 minutes East down I-195, offers a little more in terms of culture than Fall River (though not as much as Providence) as well; some good restaurants, nice museums and art galleries and a fascinatingly historical and beautiful downtown with cobbled streets centered around the New Bedford Whaling museum. Newport R.I. is about 1/2 hour away and is a fantastic time as well.
Again, Fall River isn't too special on its own, but it's not devoid of activity either. I've always thought the biggest advantage of Fall River was its proximity to other things. It's only minutes from Providence, New Bedford, and the Ocean. It also has a nice state forest that it shares with neighboring Freetown.
I grew up around Fall River and have spent the past 4 years in Portland, ME so I know what you're leaving. You will be able to find much of what you loved about the Portland area in the Fall River area and probably a little more.
Some pictues I have of some of the previously mentioned communities:
Assonet (the Assonet Bay):
Westport (Horseneck Beach area):
You can find more pictures of Fall River on the last page of the "Massachusetts Photo" thread as well.