I'm full of opinions and I know how to use Microsoft Paint, so I decided to make maps of where I'd like to see the NYC subway system go. I have no idea how feasible any of this is, and the routes shown are probably not the best possible, but it illustrates some principles I'd like to highlight.
#1 - There's no east-west train connection across the Bronx
#2 - There's no direct train connection between the Bronx and Queens
#3 - No train goes into LaGuardia Airport
#4 - The "G" train is one of the few that directly connects Queens and Brooklyn, and it would be cool if it went farther north
#5 - That Verranzo Narrows bridge really should have some rail transit on it (Damn you Robert Moses!)
#6 - Staten Island doesn't have enough rail transit, and unless that changes it'll always be your most suburban borough
#7 - Too much of your transit forces you to go into Lower Manhattan to get anywhere. It's time to focus more on connecting the other boroughs together!
Oh yeah, and 100% of the new stations should be accessible to the disabled and people toting strollers, bikes, etc.