Haven't been to Alfredo's in a while. Our last experience there (many years ago) was underwhelming. So underwhelming that it has kept us away. We found it to be rather expensive for average italian food that we can get a lots of places at home. It was also crowded and noisy, and this was back in the days before we had kids and were looking for quiet roamntic places. That being said, I have read some recent good reviews, so who knows - maybe we'll give it another shot.
We ate at Palio's a couple of years ago. Nice atmosphere, good food, and a decent price for the experience (although it is not the cheapest place in the World). It was a better experience than our dinner oh so long ago at Alfredo's. As for kids at Palio's - no problemo. Our daughter was 2 at the time and she was absolutely fine. Only you know your kid, and if you don't think they are capable of sitting thru a nice meal in a nice restaurant and you feel you might be uncomfortable worrying about that you may want to reconsider. Other than that there is no reason to think twice about bringing a child there.