Research for a possible move

The smaller capitals in the Northeast -- Natal, João Pessoa, Maceió, and Aracaju -- all have a lot of charm, a relaxed lifestyle, nice beaches, and are within easy reach of Recife and/or Salvador.  The same can be said of Olinda, the old colonial city in the Greater Recife area, although the cost of living may be a bit higher.
Security is a concern anywhere, and with the economy still in the doldrums, it's not improving quickly.  Still, it's mostly a matter of choosing the right neighborhood, and exercising street smarts while you're out and about.
Enjoy your research -- it should be fun.

Florianópolis, SC may be an option. How close to the coast? Costs will drive your area.
Curitiba is 1.5 hours from the coast.
As abthree said staying in the NE is nice. Just be sure to seek comments on crime, health care and banking systems and such. American Expat should research getting funds from US to BR.
If any banking ties will remain in US think of a telephone carrier. Many banks and such do not accept calls from a skype #. There is a thread on this subject. I ran into this issue and many here helped.

Tex makes a good point about phones:  be sure to look for that thread.  I ported my US number over to Vonage, and can call any number in the US or the world as if I'd never left Illinois.  The box plugs into our broadband router, VOIP.  Can also make and receive calls on my Brazilian cell, through the Vonage app.  Check it out to see if it makes sense for you.

Terry,
With respect to your questions on the Welcome thread"

"1. How do you deal with finding certain things that you miss from back home.   I spent the past 8 years living in Europe (4 Kosovo,  4 Germany) and became quite familiar with Amazon for shipping items.   After reading a couple responses above about import tax don't think that is an option.  What are y'all's solutions to this.
2.  Bringing a family pet.   Has anyone brought their dog with them.   I have an Alaskan malamute that I would love to bring if I relocate.   Problem is size ( think 55kg with a double fur coat) and the heat. "

1.  Important question:  will you be shipping your household goods to Brazil, or are you planning on starting from scratch here?  If you're shipping,  there's one set of advice, if you're not, it's different.  Your inference is right about Amazon, though:  the taxes and fees for ordering from the US for delivery in Brazil are prohibitive, and Amazon Brasil is still mostly a bookstore, although that is changing.
2. From everything I've heard and read, Brazil is pretty liberal about bringing pets in; in particular, they don't generally require quarantine.  There will be paperwork requirements, though, which the Brazilian Consulate should be able to clarify for you.
The bigger question will be your pup's health and happiness in the climate in most parts of Brazil.  As you narrow down your moving preferences to a limited number of cities and states, check out the monthly temperature highs, lows, and averages throughout the year (you can usually find them in the Wikipedia article on each city), compare them to the Summer temps your dog is used to, and maybe discuss them with your vet.  Dog grooming is available in Brazil, at least in the capitals and larger cities:  the solution may be as simple as a permanent brushcut!
Rabies is endemic in Brazil, and canine distemper is a serious problem in many regions:  to transport him internationally you'll need to have his shots up to date anyway, but those are two big ones to keep in mind.

Thank you very much for the response.
I will probably not be moving anything with me but I will check moving companies just to see a price.

In talking to moving companies, be sure to ask them whether they have specific experience moving clients to Brazil.  Navigating Brazilian Customs with a household shipment is a complex, intricate, and time-consuming process, and the slightest error can result in long delays and high costs.  As  one mover said to me, "I used to think that China was the hardest country to move someone to, but I learned that it was Brazil,"  Someone without Brazil experience, even if they have overseas experience, will probably lowball you, whether they mean to or not.
Most things you'll need for daily life, or reasonable substitutes, you can find here.  If all you're bringing is suitcases full of clothes, I'd suggest tossing in all your small kitchen gadgets, and, if you like to cook, a set of measuring spoons in English measures.  If you decide to use a mover, we can circle back:  there are additional, larger things that I'd suggest throwing into the container.
If you don't have permanent residency yet, be sure to check the list of documents that you'll need to bring to the Federal Police to get it, and obtain them, with apostilles where needed, before you leave the US -- it will be much easier.  You can get sworn translations in Brazil, but getting the original documents at long distance will be a hassle.

I looked into moving items to brazil and the costs door to door was more than the items were worth. Even told since I was so near PY it would be cheaper to ship from Santo, BR direct to PY, but the customs entering BR from PY could be an issue.
Only brought a tv (biggest item) and extra luggage with some items I knew I could not find in BR. Would have moved washer & dryer, but with no hot water (unless pay an "arm and leg" from water heater for house) I decided no.