Thanks for the link to my blog post.
Belleayre only has 1 high speed lift. The Tomahawk is a fixed grip quad.
Campgaw is a great place to start. I learned to ski there and so did my kids. The magic carpet is short and very mellow. One of the double chairs has a midstation about 2/3 of the way up so you do not have to navigate the steeper top section.
Tuxedo Ridge has only run the Bunny double and the Tiger double when I have visited with my kids. It is a fun place that offers some longer runs than Campgaw.
Mt Peter skis is also another good choice for learning to ski. It is a few miles past Tuxedo Ridge.
Thunder Ridge is much larger than the Campgaw/Tuxedo/Mt Peter. There is a steep drop at the very bottom of the area. Almost every other trail can be handled by green skiers.
I also spent many days as a youngster skiing Vernon Valley/Great Gorge, now known as Mountain Creek. While it can be entertaining, I have not been back since 2001. It can be very crowded on weekends. I would rather drive the extra 1/2 hour to get to Belleayre or Hunter. Plattekill and Windham add another 15-20 minutes. Despite living in NYC/north NJ, my kids have not been to Mtn Creek.