Come watch the classic game of Bocce Ball and eat great italian food.
Piazza Italia is one of our favorite places and I have recommended it for friends who have kids. The food is fantastic (voted the best Italian in Portland several times).
The place is pretty small, so if you are going for lunch you are usually fine without a reservation. If you are going for dinner, you will need to make a reservation, otherwise you won't get in.
Ever time we have brought our guy in they always greet us with open arms (and coo over him). They always make sure we have plenty of fresh baked bread to keep him happy. When all of us families came in and they ran out of highchairs, they started bringing out huge stacks of fabric napkins for the kids to sit on.
There are loads of pasta dishes, and very friendly kids versions that they will make special upon request (our guy LOVES "Gino's Favorite Dish" - Linguini Squarciarella). They will do special half portions for your little ones, and if you feel like you need a little more, they will do a portion and a half (you just have to ask for it!).
The place is also noisy enough already with the hum of the restaurant, that kids are hardly noticed. Futbol fans will enjoy the games playing on the big screens and the italian music playing (usually opera or some combo of opera and more modern music).
The only thing they don't have that would be handy are changing tables for the smaller kids, but we have been fine without them.
After dinner, a walk around the Pearl District is a nice way to finish the evening. Jameson Square Park is a block down the road, and has a great fountain that runs in the summer.