It's not my favorite restaurant, but Hogshead BBQ has always been pretty good about letting us bring the dogs. Noodles and Company is also nice since they have the big patio.
For a quicky, the family and I like to order "to go" food and sit on the wooden patio by Brugge and watch passersby on the Monon. It is also conveniently near the Sno Cone Shak for a refreshing summer dessert.