If you want to roll around the City, ditch the bike and take your Rollerblades. I used to go into the City on Sunday mornings with younger daughter and go down esplanade along the Hudson, into China Town, etc. Also Central Park. When done, 'blades go into backpack and you don't have to schlepp yer bike. I remember one conversation: Dad: Watch out for the dead rat. Daughter: Didn't you see the one you almost ran over in Bryant Park??? Ahhh, the City.

Here's a couple of links: http://www.nyc.gov/html/edc/pdf/greenway_mapside.pdf
http://www.nyc.gov/html/dcp/pdf/bike/mapfront.pdf