Hi Linda, I am a single, professional woman and also a Nashua native. I think your best bet in Nashua is the Exit 8 area. Kessler Farm is particularly nice and is in a perfect location for commuting- and they allow small dogs. Although there's no train service from Nashua to Boston (yet), there is a great bus service (with free wifi) that leaves pretty much on the hour going to Boston, with 2 main hubs- one on exit 6 and one at exit 8. Even if you want to drive- it'sonly 45 minutes to Boston, however during rush hour, it's rather busy. And there's always the option to take the train into Boston from the Lowell station.
Nashua's Main Street has lots of nice places/restaurants and several "adult beverage" establishments you can enjoy.
Although there is mention of Hudson in some of the responses, I wouldn't recommend it.
I wish you lots of luck with your move!