There are groups for dads at the 92nd St Y. I went to a New Dads/New Babies group on weekends. There's also a New Parents Get-Together, on Wednesdays I believe, that is open to both moms and dads. I haven't been myself but my wife has mentioned that some dads do attend.
Otherwise, another way to meet other parents and babies in group settings is to attend play/music activities at places like Gymboree or baby swim lessons at 92nd St Y or Asphalt Green. For better or for worse, you'll likely see more moms than dads there during the week, with more dads attending on weekends, but they are certainly open to all, and I have enjoyed attending these with my daughter.
Good luck!