You'll be very close to Marina Bay which has a boardwalk with a few nice restaurants, and there is also a nice little park with some walking trails along the water and nice city views in the Marina Bay area too.
Quincy Center is a quick ride down Hancock Street, and there are also some nice restaurants and bars there. Q Center has some range too. You can make it a family night at a nice restaurant, but there are also a bunch of bars if you are looking for a night out with friends. Fat Cat is one of the more popular restaurants in Q Center and is also one of my personal favorites - amazing chicken wings and lobster mac. Fuji in Q Center is an amazing Japanese place with great sushi and nice ambiance. Alba in Q Center is supposed to be nice for Italian, and I think they have a roof deck, but I have never been so I don't know. Remmicks is newer restaurant in Q Center that I have heard good things about, but I haven't been there either; from what I have heard it is very lounge-esque. Brother's has amazing roast beef and pastrami sandwiches. There is also a Four's and Stadium Sports Bar around there, if you are looking to catch a game.
I'm pretty sure there are a lot of walking trails right around your building. I know that there is a large park on Neponset River, but I have never been there, so I can't tell you how to get there. It looks nice from my boat though.
You're also a short drive to the South Shore Plaza and AMC movie theater in Braintree. There's a bunch of restaurants around there too, including a Cheesecake Factory.
A little farther down the road is Legacy Place in Dedham which I'm sure you have heard of.
Tony's Clam Shack on Wolaston is amazing and Wolaston is a nice place to go for a walk with the family. Also, Baby Cakes on Beale Street has amazing cup cakes if you're into that kind of stuff.
Quincy is pretty small, but there is a lot to do. I have lived here for about 5 years, and I am still finding new things. I found Quincy to be a great little alternative to Boston, and I hope that you enjoy your time here as well.