Within Poughkeepsie itself: I’ll second, or third, or fourth, the following:
*the Walkway Over the Hudson–easily accessible, great view, nice way to spend an hour or so (depending on how fast you walk)
*the Vassar College campus–very pretty, some great buildings, check out the Old Observatory with the statue of Maria Mitchell and the maze of stone staircases in the front section of the library, also Sunset Pond (they call it a lake but it really isn’t)
*the CIA, if you’re into fancy cooking–the best part is being served by the extremely enthusiastic students who (sometimes) created the dish
Also: the Hudson River, in general; though the city waterfront is only partly parkland, and the green space is divided into disconnected sections, and the most impressive feature (a place called Kaal Rock) is really not a nice place to visit, it’s a fine place to spend some time. The Marist College campus, though overshadowed in many ways by Vassar, is right on the river, with very nice views and a lovely little park that runs between the train tracks and the river itself. A terrific place to stretch out and read. Check out the main boathouse if you get down there.
Museums: the Clinton House and the Glebe House are small historic houses in edgy parts of town (you won’t get killed, but they do look a little out of place)–you wouldn’t spend lots of time in them, but they can be interesting. Old mansions–the Young-Morse (as in Samuel) Estate, a place called Springside, others further north along the river, if you’re into that sort of thing. The Vassar art gallery. It’s not the most museum-rich area in the country, but it does have a few things. The area has a long historical heritage–the city was incorporated over 300 years ago–and the past is evident in the architecture etc., though not much survives from THAT long ago 
Foodwise, Poughkeepsie is an excellent place for Greek diners–they have 'em elsewhere in parts of the Northeast, but not so much in other regions. Lots of chrome, lots of neon, menus that go on for pages, quick service, open 24 hours (you see some very interesting people at the Palace Diner, in particular, at 2 in the morning), food that’s better than you might expect. There’s no single local specialty, which is too bad, except shad/shad roe, which appears pretty much only in April/May; anything called “Hudson Valley ___” (such as salad, sandwich, etc.) is apt to contain apples, which are an important crop in the area, and possibly cheese (dairy farming used to be big). Up and down Main Street and just off it there are a lot of little ethnic places, Jamaican, Ecuadorian, Vietnamese, little hole-in-the-wall delis and cafes, and of course Mexican; language may be a barrier, but the food can be awfully good. (The City of Pok is ethnically pretty diverse. The rest of the region, with few exceptions, is not.)
A little further afield: folks have mentioned Mohonk Mtn House, and FDR’s home and library, and the Rhinebeck Aerodrome. Also New Paltz if you’re into towns that are still in the seventies (though they come by it honestly), and West Point, though it’s much harder to get a look around than it used to be. I’ll throw in the Vanderbilt estate, also in Hyde Park, as well. In general, Poughkeepsie is a terrific place if you like the outdoors: lots of parks and hiking trails, most of them very well kept up (the Appalachian trail runs through the county, about a 20-min drive from Poughkeepsie), a few rail trails, the river for kayaking etc., rock climbing at Mohonk (the Preserve, which is separate from the Mountain House). No, it’s not the Canadian Rockies, and there’s no beach anywhere, but there’s a lot to do outside regardless.
I don’t know anything about clubs, but theater is quite strong in the area: Powerhouse is a pro company that takes up residence at Vassar each summer; Boscobel, south of Pok in Garrison/Cold Spring, does mainly Shakespeare; Marist has a professional rep company doing things this summer. They aren’t necessarily cheap, so I haven’t seen most of them.
You should absolutely have a car, if at all possible. Public transportation in the area sucks. (Okay, there are places that are worse, but it’s not good.) There are lots of little tiny cab companies in the City of Poughkeepsie, but they can be pricy and not always reliable.
I’ve lived in Poughkeepsie for…many years now. Tourism is actually a much larger industry in these parts than some previous commenters might lead you to believe–not in Poughkeepsie directly, though that is certainly on the upswing, but in Dutchess County generally and in the region as a whole. A lot of that is daytripping and long-weekending, and a lot of that is folks from NYC, NJ, Philadelphia looking for something to do fairly close to home; it doesn’t tend to be the two-week-vacation kind of thing that people might take at Cape Cod, or DC, or Hawaii, or some other more standard tourist destination. But if you’re the sort who’s able to enjoy new surroundings just for the sake of new surroundings, which it sounds like you are, and if you’re willing to explore a bit beyond the confines of the city and town of Poughkeepsie, and it sounds like you are, and especially if you enjoy outdoor sports and very pretty if not necessarily breathtaking scenery, then you will have no trouble occupying yourself for a month.
If I think of other things I’ll try to remember to post–and I may be able to answer more specific qs as well, if you have them. Good luck!
