Rochester is one of the Medway towns(Gillingham and Chatham are the others). A significant price increase is probably the only reason to live there. Rochester is probably the least chavtastic of the 3, there are almost certainly nicer bits but that's the same everywhere. There are lots of nice bits of rural Kent but these may not have the convienience you need if you are commuting daily.
EDIT: I have never lived in Medway but my job takes me to sites all around the area.