You'll love Louisville! I've lived here all my life and I never get tired of it!
What area of town are you moving to?
One neighborhood that's appealing to most Craftster types is the Highlands, specifically Bardstown Rd. They've got a lot of good locally-owned restaurants and funky shops, including the Knit Nook, Edenside Gallery, and vintage/DIY clothing places like Cherry Bomb and Dot Fox. The area is just southeast of downtown.
As far as fun and artsy places, I love Main Street: be sure to check out the 21C Hotel/gallery and the Kentucky Museum of Art and Craft (both have free admission). And they are right by the Waterfront, which would be a great place to go with your daughter as there are playgrounds and fountains.
As a fiber artist, it is probably imperative that you see at least one of Penny Sisto's quilts (which are more like paintings that happen to be assembled with a sewing machine). She lives in southern Indiana, so she's done loads of commissions for various places in Louisville--I know there is one of hers right inside the door of New Directions Housing Corp. and one in the church right next door to Casa Latina on Woodbine St. Anyway, if you ever come across her name anywhere in Louisville, make a point to check it out!! She's incredible!! **End tangent**
As far as crafty supplies, I highly recommend Dee's Crafts on Shelbyville Rd. You have to fight tooth and nail through mall traffic to get there (), but chances are you'll forget about it as soon as you step inside.
To sum up, Louisville's got a pretty good downtown scene. We have nice, big urban parks such as Cherokee, Seneca, Waterfront, and Iroquois. Our zoo has an albino alligator and a newborn elephant. The Crescent Hill Library has a big purple castle in the children's section. You can watch Shakespeare plays for free in Central Park during July. Aaaaaaaaaaannnnnnd... you can get ridiculously tall orange soft serve cones at Dairy Kastle on Eastern Parkway.