Our team loves the local malls when we travel. They break up into groups of 3 or 4 and just go. The parents will wander around, window shop and generally people watch. We meet back at the food court every hour to make sure that everyone's accounted for. The last one we went to on a rained out tourney day had an indoor miniature golf course and arcade. The girls loved it! Another one we went to had an indoor racing track and they raced electric toilet carts. Yes, they were actually motorized toilets. You never know what you'll find on the road at the malls.
Another thought is Barnes and Noble. They usually have a good coffee shop and a great lounging area to check out some books you might want to purchase or just spend a couple of hours reading and relaxing.
Last but not least, the local BW3's or equivalent sports bar. Grab a beer, some wings and watch softball all day.
First option was always the movie theater. Second options were bowling or the mall. At this point all of our players are 16+, so they usually get into groups and decide what to do on their own....
It gets easier as they get older. Less babysitting, more just sitting. 14U the girls are happy to shop or hang out together with their phones--in silence.