An old shipmate of mine is coming into Asheville soon. He asked for some recommendations for things to do with his two 3 1/2-year-old kids. I checked with an expert (a friend of ours who has three small kids), combined them with my own recommendations, and thought I'd share them here.
Downtown Asheville. Downtown is very walkable. Most of the buildings date from the early 1900's to late 1920's and have been fixed up. Tons of restaurants, coffee shops, stores, galleries, and so on, most of which are local and not chain stores. The fun part is bounded, more or less, by I-240 on the north, O Henry Ave on the west, Patton Ave on the south, and N. Spruce on the east, with another nice bit on Biltmore Ave (Hwy 25) running a few blocks south of Pack Square.
Health Adventure (www.thehealthadventure.org). It's right in downtown Asheville on Pack Square. It's a participatory, hands-on, interactive, science-oriented place that explores health, biology, and physical sciences. Lots of fun for kids. Open 10-5.
Splasheville. This is in Pack Square, next to the Health Adventure. It shoots random jets of water in the air. Kids can run around in it and get soaked. Better bring some towels and dry clothes. Read about it and some other water-oriented attractions at:
http://blog.exploreasheville.com/2011/05/budget-friendly-ways-to-cool-off-this.html
Carrier Park. This used to be the old Asheville Speedway. When it closed, the city turned it into a park, with a large playground, volleyball, basketball, picnic areas, nature walk, river overlooks, more. Located at 220 Amboy Rd on the west side of Asheville.
WNC Nature Center (www.wncnaturecenter.com). This showcases the natural features of western North Carolina. It includes a petting zoo. You can see coyotes, bears, and other critters, too. Located on the east side of Asheville; a bit hard to find but they have directions on the web site.
River Arts District (www.riverartsdistrict.com). This is where I used to have my studio. It's the old industrial area along the French Broad River. Most of the industry has moved out and been replaced by artists: painters, potters, woodworkers, sculptors, you name it, they're there. There will be studios open - some are open 7 days a week, others catch-as-catch-can. Some great places to eat down there, too: 12 Bones Barbecue (won a national competition on Good Morning America), the Clingman Cafe, and White Duck Tacos, to name three. Plus a brewery.
Mountain Play Lodge (www.mountainplaylodge.com). It's an indoor play center located in Arden, just south of Asheville on Hwy 25.
The Hop (www.thehopicecreamcafe.com). Homemade ice cream in sometimes strange but really good flavors. The kids will probably go for vanilla or chocolate, but the adults can get things like salted caramel, nutella, avocado, mustard, or whatever the flavor of the day is. Two locations, one on Haywood Rd. in west Asheville, the other a mile or two north of downtown on Merrimon.
Asheville's a great place and all the above just barely scratch the surface. If you know of other cool things to do with kids, post a comment!