I live in Rhinecliff so know (or know of) a number of places:
1. Twist in Hyde Park (down 9 about 2 miles before CIA) has a CIA grad as its chef and has great buzz.
2. In Rhinebeck itself, Gigi (which another poster mentioned) is quite nice. It's upscale but not too so -- a good wine list, lots of utilization of local products, and so on. It's 5 minutes from Beekman. Turn left out the door and go up the street.
--Fosters which another poster mentioned is good for quick, cheap food -- lots of fried items. It's burgers and fries and pitchers of beer basically although it has a few more upscale things than that.
I've heard good things about Le Petit Bistro just a block from Beekman although I've heard also that it's overpriced for what it is.
I'd avoid China Rose in Rhinecliff which people flock to but which seems to me to be no better than a PF Changs type chain,
If you have a car, the next town up from Rhinebeck, Red Hook, has a lovely Italian restaurant called Mercato. You go up 9 and turn right at the intersection in town. I've had 2 meals there and liked each.
If you go back out East toward the Taconic from Rhinebeck, there's a Greek place called Diaspora about 5 miles away which I liked as semi-upscale but not too much so.
The Thai place in Rhinebeck has gotten mixed reviews and seems overpriced.
If you want to say a little more about the kinds of things you want, I can try to come up with more detail or other ideas.