Even shorter term improvements can greatly improve subway service. First, make train doors close faster. That greatly decreases the chance that someone will have enough time to both realize the doors are closing, and stick a hand/leg/other body part in. That increases reliability and reduces delays. Second, make the trains go at normal speed. The NYC Subway is ungodly slow: your typical local train reaches a top speed of just 30 mph right before braking for the next station, and an express can get up to 35 or even 40 on a reasonably long and straight track. There are a few trivial modifications that would have to be made to train control systems to allow trains to reach the speeds that they used to, and the signal systems might have to be redesigned, but probably not by much. And finally, the last improvement is not to throw out old trains when new ones are bought, and instead use them to increase peak hour service.

In the long term, upgrading the subway signal systems to some sort of automatic cab signal system system (kind of like what the LIRR has had since the 50s) would increase line capacity, and allow even faster speeds up to, say, 75 mph. And for system expansion, perhaps Madrid's $150 million per mile subway construction is a good model to follow. Of course, it would help to develop NYC's surface transportation network too, and for that I think the best option is light rail on busy corridors not served by subways, trolleybuses where light rail is not justified by demand, or where there is a parallel subway line, and buses everywhere else.

I suspect what you need is revived El Trains.

Also possibly some kind of radial railway linking Queens and Brooklyn?  As the centres of those boroughs are redeveloped as 'satellite cities'

I can see the lawsuits though-- this being America, and this being New York ;-).

I am (still) amazed that you let SUVs onto Manhattan during the peak hours.  We do too mind, but the Mayor wants to raise the Congestion Charge from them from £8 to £25.