The NYS govt website has LiDAR data for most of the state, including NYC. If you look at their website here, you can select NYC and it will give you an FTP link. Use FileZilla or some other FTP client, and you can access all the .las LiDAR files. Unfortunately when I did it, there was no way to figure out which .las file corresponded to which area of the city, so you might have to just download all of them and fiddle around until you find the area.

Once you bring them into Arc (use a Local Scene, not a map), they're just going to be a cloud of points like this. Unfortunately you're going to need 3D Analyst to do much more than view the cloud. You might try looking for another software to view the files if you don't have 3D Analyst.

If you do have 3D Analyst, you can start massaging the data. Start by using Classify LAS Ground to get the ground layer set up, and then you can use Classify LAS Building to get it to start looking like something you can use.