My husband and I rented a scooter in town to drive around the Plain. I would not recommend visiting on foot, because it's so large (unless you really, really like walking all day). A bicycle or scooter is a really good way to go, but there are gravel roads, off the main paved roads, that we couldn't drive on. There are scooter rentals in the harbor area of Stari Grad, but they are not cheap (priced for tourists).This is an ancient agricultural plain, and I believe it's the oldest in all of Europe that is still in use. The same farming technique has been used for over 2 millenia. There's not a lot to see beyond the olive trees and fields, but it's a really nice experience, with calming and relaxing scenery and a beautiful countryside.
Great and quite place
Must see place in Stari Grad. The ticket is 15kn, during the summer it's open during the morning (I think 'till 12) and again in the evening. Quite and great little place to visit and to learn more about a big croatian writer.