Since you're visiting the city and have limited time, maybe you should try to see the city instead of chasing suburban hills, (though the Alpine ride described before is OK and won't take up too much time.

Possibly the toughest hill in Manhattan, and maybe the whole city excluding Staten Island is Fort George Hill, in Washington heights.

It can be part of a nice ride around Manhattan. Head up Riverside Drive. At 165th Street you'll need to get on the bike path, and continue up to ****man Street, which will take you to the foot of Ft. George Hill. Between 165 and ****man, you might climb up to see the Cloisters. You'll need a lock if planning to go inside, but the grounds are nice to explore.

Once you climb Ft. George Hill, follow the road south and go to Highbridge, which was one of the original aquaducts serving Manhattan and has recently been restored as a bike/pedestrian only bridge to the Bronx. It's worth it just for the view. Then you can head down the hill and pick up the East side bike path to complete your circle of Manhattan. Coming back north don't go straight to the Hudson River, but instead stay more central, so you can explore the various neighborhoods of lower Manhattan, making sure to sample the great food.

Also keep in mind that NYC's bridges are among the highest hills in the city, so be sure to Ride across at least one. Probably the Brooklyn Bridge is the best choice of the East River Bridges. You might use it and the Manhattan Bridge to build a short Brooklyn side loop into you Mahnattan tour.

The fact is that there's plenty of good cycling in NYC. Not the kind of open road scenic riding we look for in the country, but the city is chock full of worthwhile destinations, all accessible by bike. I don't think it's possible to come close to exhausting the option in a week.