I've ridden the trails at Minniwaska.
YES you can do them with a cross bike (or a MTB)
Lakes, views, waterfalls, great stuff, Highly recommended!
New Paltz town is good for restaurants. Yanni (Greek) on Main St is my fav.
A lot of great road riding along rivers, farms etc.
I was up there this weekend (road bike.)
There is also a cool looking rails to trails thing up there that
looks very doable by cross bike, as mentioned by fiamme_red
This website has maps of the area:
http://www.roberts-1.com/bikehudson/...#text_list_all
good luck
VF