Woodpecker Way playground "Tiddy Brook" is one of the smaller and newer playgrounds we visited. It's next to the road, but fenced in among some lawns around a tree-lined cycle path and stream.
There seems to have been some good work done on linking the roads in the area with footpaths and cycleways. It's certainly more navigable than Google Maps - in June 2012 - would lead you to believe. There's a direct, off-road route from the Bishopsmead playground to this playground, suitable for a road-bike and trailer.
View Tavistock playgrounds in a larger map
My kids enjoyed the high-quality, modern play equipment very much, even
though we were there on a miserably soggy day with frequent rain
showers. They spent as much time sheltering under the "crow's nest" as
they did playing on it!