The Water of Leith is a short river that runs from its source in the Pentlands to the Firth of Forth at Leith. There’s a path along most of it, starting at Balerno and finishing at Leith. It’s about 13 miles (19km) and flat so it’s an easy day’s walk.
As it’s a linear walk, I think it best to use Edinburgh’s excellent buses rather than a car to get to the start. The 44 bus runs from the city centre to Balerno where there’s a sign to the walkway.
From Leith, there are lots of buses to the City Centre and to the south of the city. I caught the 16 back to Bruntsfield.