Shediac, Cap Pele. 15 and 25 minutes from Moncton respectively. Beautiful beaches, friendly people. Shediac is quainter, nice restaurants. Beaches in both areas are stellar. Parlee Beach in Shediac, Aboiteau Beach in Cap Pele.
Other options, St Andrews - 30 minutes from Saint John. Quaint liltle town, dead as a doornail in winter though. Basically anywhere in southern New Brunswick you will find a myriad of little towns that are near the ocean and scenic, and within easy driving distance of Moncton, Saint John or Fredericton.
Also, if you are open to Nova Scotia, check out the Annapolis Valley (sp?)- just suggesting that due to fruit growing. Closest city would be Halifax. There are lots of lakes and rivers everywhere in the Maritimes.
I would suggest you look on
www.propertyguys.ca and
www.kijiji.ca for homes as well. Selling ones own home without a realtor is hugely popular in NB and you will find a lot of homes that aren't on MLS (realtor.ca) there. I have bought and sold lovely homes with Property Guys in particular.