How about a museum exhibit you've wanted to get to or a botanical gardens, as you are looking around you are walking and talking you are able to enjoy just being together. Many have nice cafes and beautiful places to sit. Some have once a month free days so that could save you some money.
It's a lovely idea, girl's day out, it's what memories are made of, and memories are the duct tape of relationships. I am sitting here wishing I could have a girl's day out with my mom and sister...
Hope whatever you do, you have fun just being together.