I'd extend the Victoria Line to Chingford. This would free up some paths into Liverpool Street... and get rid of a stub that annoys me.
I'd split the Northern Line, because it makes sense. I like my Tube Lines to be neat and branches do not equal neat.
I'd suggest that any new line should be similar to the Victoria Line. As in, it would have as many interchanges as possible.
I'd also suggest that the next new line run via the West End, with a new station in Soho and a new/reopened station at Aldwych. I know these places are close to Covent Garden/Leicester Square/Charing Cross, but I think think those busy stations would be given some much needed relief if there were more intense services.
Away from the Tube, I'd extend the DLR to Dagenham Dock, as was suggested before the recession bit.
I'd also like to investigate extending the DLR from Stratford to Kings Cross/St Pancras. I'd do this by running along the North London Line until just past Kings Cross, then running to an above ground terminus called Kings Cross St Pancras DLR. The new station would be between the mainline stations.
If I had a lot of money and didn't have to worry about planning permission, I'd love to bulldoze every GOBLIN station. I'd replace them with new stations where the GOBLIN cross other lines, thereby creating interchanges. Currently the GOBLIN crosses a handful of lines, yet makes good connections at only Barking, Blackhorse Road and Gospel Oak. Every other connection involves a street walk. To show you what I mean, I'd bulldoze Woodgrange Park (GOBLIN) and Forest Gate (NXEA) and possibly Manor Park (NXEA) and build one station with a low level and a high level. To do the whole line would cost a fortune, but I dream of the day.