For someone living in South Tyneside and all the issues with Metro at the moment I have always favoured some kind of tram system running on the West side of Newcastle, maybe linking in the Metrocentre on the Gateshead side, the tram would link up to an interchange with Metro access, kind of like Heworth currently is, then a separate tram system turning Pelaw into an interchange with the tram line running on the current old leamside alignment to Washington with slight on street working but going no further.
I am also an Aberdonian and always thought that some kind of underground or metro/tram system would be ideal, one line from Dyce/Airport to somewhere like Balnagask/Altens/Cove Bay and an East to West line going from the Beach to somewhere like Mastrick via Hazelhead both lines would interchange at Guild Street for onward travel by train or bus, Aberdeen is big enough that Tram/Metro working would and should work.
And Medway, what can I say about the Medway Towns, OK I was last there 20 years ago but there were so many places crying out for transport links, Gillingham Business Park was one especially and so was the Medway Valley Leisure Park, 2 railway lines either side of the Diggerland site Albeit one is HS2 but there is no station on the Medway Valley Line and when I was there, no bus service, I used to work in the Bingo hall that used to be there and it was a nightmare if you didn't have a car, it always seemed busy but it could have been busier.
The route I would run, would go from Medway Valley Leisure Park, run along possibly beside the current Medway Valley Line through Strood via the station, onto the edge of the city estate, through the tunnel round St Marys Island via the Outlet Centre then along Pier road,to The Asda like previously discussed on this thread along the old Gillingham Dockyard alignment to Gillingham station or potentially on to Yokosuka Way.
In all honesty, doing any system involving crossing the river to encompass Rochester would involve another bridge or tunnel, I like the idea of splitting the lines between Delce Road and City Way, another option may possibly be a loop from Maidstone Road at the Airport end at The Tideway and then along Arethusa Road to link to City Way or even better, running up the Rochester Maidstone Road (B2097) along the M2 side of the airport, onto the roundabout and then down the Chatham Maidstone Road (A229) then City Way, You could have made more of a loop down to the esplanade if the Borstal road Junction from Priestfields wasn't so tight, and Shorts Way has a restriction which would probably not be welcomed by a tram line.