The hospital apartment is definitely subsidized. I highly doubt you will find a market-rate 1BR in a doorman building south of 96th Street for less than $2000/mo, and it can be difficult to find one for less than $3000/mo in a building/area you actually like. That said, it can be annoying to get between 70th/York and Columbia's Morningside campus, since you'll have to take both a crosstown bus and a subway (or two buses).

While there are some pretty questionable areas in Washington Heights near the 168th St campus, there are also some decent areas (even some really nice areas along Ft. Washington Ave), and it's much easier to get from there to the Morningside campus than from 70th/York, since it's just a subway ride (no crosstown bus). You may be able to find market-rate housing up there that's roughly the same price as the subsidized housing at 70th/York.

If you have time, I'd say it's worth beating the pavement up in Washington Heights before you commit to 70th/York to see if you can find something acceptable up there. If not, however, 70th/York is a perfectly decent area, the commute isn't that bad, and the price will be very hard to beat.

As for getting to Linden, Zipcar isn't cheap, but if you're only out at Linden for a couple hours, it may make sense for you. It's $50/year + $10-12/hour on weekdays. Plus you'll pay tolls of ~$2 each way for the Turnpike + $6 for the bridge/tunnel back into Manhattan (leaving Manhattan is free). Gas and insurance are included. That's more expensive than public transit, but I'm pretty sure it's going to be cheaper than keeping your own car in the city--unless you're staying out at Linden for several hours at a time. Driving will probably cut an hour off your journey compared to public transit, as long as traffic isn't too bad. You may still want to consider public transit, however, as the trains are generally much more reliable than tunnel and Turnpike traffic, and you might be able to get some work done on the trains.

Zipcar is not that useful for shopping, as you can walk or take public transport to almost everything in Manhattan, and parking often costs more than a taxi if you can't carry everything home. Most Manhattanites live perfectly happily without a car. If you're serious hikers a car can be useful, but there are also good guides available for hiking directly from MetroNorth train stations without a car. See, for example, http://www.mta.info/mnr/html/getaway...d_gohiking.htm