I'd like to echo Recchia and throw in my support for living near the Providence/Pawtucket line at the top of Blackstone. I've lived here almost a year and I've felt safe in my neighborhood and love the proximity of the Blackstone path. There are a number of good restaurants within walking distance and a Shaw's grocery store I walk to sometimes (although that I would only do in daylight) as N. Main can be sketchy after dark.
The rest of Providence is an easy trip down N. Main, Hope, or Blackstone Blvd depending on whether you want to end up downcity, Thayer/Wickendon, or Wayland, respectively.
Almost everyone on my block has a dog, although the nearest dog parks seem to be the one behind Hope High and Rainbow Park at the other end of Blackstone. Lippett park is right near me and there are lots of dogs - just not off-leash.
Warning: these neighborhoods are pretty quiet and there is NOTHING in the way of nearby 'nightlife'. The pubs on Hope are within walking distance, but they don't stay open that late.
Best of luck with the move!