While I like Italian, I rarely seek it out so of that list I have only been to La Viola.
That said, I love La Viola, and have been more than once. It's simple, inexpensive, and just plain good. It IS loud, but I highly recommend checking out La Viola Oest - it's right across the street, with the same menu and everything, but usually quieter. It's basically just overfill space.
We haven't been to La Baia. I'd like to know the noise level.
Here's my take on the others:
Although we haven't been to Branzino very recently, we've gone there many times over the years. A step above - lovely ambience, very good food well prepared, excellent service. We took a group there after a family graduation and everyone was pleased.
La Viola - good food at a very reasonable price, noisy and hectic. Not for us. It's sister restaurant across the street is a little quieter, but still noisy and rushed.
Bellini Grill -very ordinary.
La Fontana della Citta - uneven. After I had brown salad greens and a dirty fork, I didn't want to go back.
You have more choices if you can include Sansom Street. Melograno, which has very good food, was too noisy for us.
If you're going to try one, I'd go with Branzino. There was a coupon today on the Center City District site for 15% off.
Of those you've listed, Branzino is my favorite. Classy atmosphere, solid food, good portions for the price, and a nice variety of dishes offered.
I like La Baia for a simple meal but it's nothing I'd go out of my way for.
I was underwhelmed by La Fontana della Citta. Felt like South Philly Italian-American instead of the authentic Italian-Italian I personally prefer, just dressed up a bit for Rittenhouse Square. And lousy bread.
Have not been to La Baia or Bellini Grill.
A little off the 17th & Pine area (but not much) I second Melograno for truly outstanding and innovative Italian BYOB. Also, it doesn't get much talk/rep around here but I am a diehard fan of Roberto Cafe at 22nd & South. Best Veal Milanese I've had in the city and it truly feels authentically Italian "trattoria" to me. My partner and I always go there when we are missing Italy and want a solid, non-fussy Italian meal.
I have only eaten 2, but they are two of my favorites:
Bistro La Baia is great. Nothing overwrought, but great, clean flavors. Good family that runs the place, always very friendly. It can be one of the loudest places in Philly though, bested only perhaps by:
La Viola! I think this takes the cake for best value in the City. But it is one of the loudest restaurants I have dined in anywhere, and you are on top of the adjacent tables. I guess that's how they keep their prices reasonable.
One potential add-on would be Giorgio's on Pine, but you'd have to cross Broad so I'm not sure if that would nullify the "nearby" distinction.