NRP is the main city park. there are a couple of ways to get there, but I would suggest Ewart Ave. because the other main entrance at Paint St. charges an entry fee (really stupid). Also, it will look like you're going through a asphalt plant coming from Robert C. Byrd Drive on Ewart because you are, but once you get through that, the park is pretty nice. Not Central Park nice, but nice enough for Beckley.
Bing Maps - Driving Directions, Traffic and Road Conditions
Two other parks with playground equipment in Beckley include Freedom Park, which has the local skate park attached, but has some nice playground equipment. Its located directly off of Eisenhower Drive.
Bing Maps - Driving Directions, Traffic and Road Conditions
The other park is Thornhill Courts, which is the smallest and is located just outside of Downtown on Second Street.
Bing Maps - Driving Directions, Traffic and Road Conditions
Also, Tamarack does not have playground equipment. Its a touristy place that sells overpriced crafty things like glassware, paintings, ceramics, and foodstuffs. They also have a toy section, but its old fashioned toys like marbles and wooden cars and trains.
Its interesting if you've never been there, but again, a lot of the stuff there is overpriced.