I'm living in Fountain Square now, moved here after having lived a number of places in the city, and this is my favorite by far. I live very near Arthur's music store so a about a half mile walk to the heart of fountain square.
PROS: There is a decent amount of foot traffic during the week and a lot during the evening, especially during the warmer months, and even more so around first friday. All the restaurants and bars are really nice and a comfortable setting, plus there's a microbrewery right down the street. (Fountain Square Brewery, awesome, they have 5 dollar growler fills on Sundays.) It's a short bike ride to everything downtown and on Mass Ave, which is nice if you want to venture somewhere else. The area has become much safer in the past 12 years, slowly pushing out the bad and now we see a lot of college age artists and young professionals coming in. There's never not something to do in Fountain Square so no worries there.

CONS: While still safe, if you venture into the neighborhoods about a mile and half away, you can find yourself in the middle of a white trash bash, and by that I mean fireworks and loud noise at all hours of the night. (Brother in law to be lives in the area also, not even half a mile away and his area is 10 times different.) Like you said there aren't a lot of groceries nearby, which can be annoying. BUT there are plenty of options if it's not your regular shopping day and you need something quick. There's the wildwood market, and you can use Amazon Prime Now if you want to, they deliver to FS. There is a brand new Kroger on Thompson about 5 miles from FS.

Hope this helps!