Took the coastal path from
Icmeler to
Marmaris on day 1 last year, and I think we only travelled the route by dolmus only once throughout the whole week!
Realastically takes about 45mins at a steady strolling pace and as already mentioned, there are plenty of stop off points and benches along the way.
As long as you have comfy footwear and are prepared for a few blisters (or 'white bits' if you're wearing sandals) then it's well worth it.
At night, it is fairly well lit, and I remember there being some amazing sights looking over the water to see the stars and moon reflecting in the sea.
Maybe wouldn't advise walking alone at night as it can be fairly quiet in terms of not many other people around, but is alot cooler at night and is very relaxing.
Enjoy!