Rochester also has direct trains and direct road to Greenhithe. Places over to the west of the county, such as 7oaks, Tonbridge, it's much more difficult to get to Greenhithe - no trains, and the roads don't go in the right direction.
The Medway does curve around, but it's more usual to talk in terms of east and west rather than north and south of it. Strood is west, Rochester east.
Pupils travel to school by bus and train between Medway Towns, Gravesend, Maidstone and Sittingbourne.
Gravesend is near to Greenhithe, has HS1 plus other routes to London. But I haven't been there for some years, so don't know what it's like now.
Have to put in a word for Margate. Yes parts of it are rundown, yes the Westwood Cross Centre killed off Margate and Ramsgate High Streets. But the coastline and clifftop walks and fresh air are lovely, the Old Town is quaint, and there are some nice properties to be had.
But it's not really in easy commuting distance - although some people do - and if Canterbury is too far out for op, Margate is even further.
(And it's Math School, not Maths School. The full name is Sir Joseph Williamson's Mathematical School.)