worst comes to worst on Metro North you can just pay the $5 to the conductor for the bike pass, or say you are getting it when you reach Grand Central. Of course if you are staying in Morningside you should get off on 125th, but whatever.
Driving is not bad, especially if you are staying uptown like it seems you are. Unless you get lost it'll hardly count as driving in Manhattan. Parking isn't awful up there either especially if you are willing to park on Riverside Drive.