Peekskill is not far from Tarrytown. Maybe 15 or 20 minutes. I grew up in Katonah, but moving to Mohegan Lake to start a family and I spend quite alot of time in Peekskill. Here are the pro's and con's.
Pro's-
-It's right by the Hudson, and the views are VERY NICE. On any given day you can look to the water and see bear mountain and "upstate" in the distance.
-It's a city that has gone through it's bad time and there is alot of effort now to "bring it back up" although it's coming along slowly. In the summer time they have something going on outdoors almost every weekend. Last year they had an awsome jazz and blues festival. They shut down the streets and everyone just listens to good music, eats good food, and has a good time.
-There's definetly something "magical" and "historical" about it. All the buildings are old, and you can picture what it was like "back in the day."
-Your very close to major highways and roads, there is alot of shopping on route 6. There isn't alot of high-end or great stores (you will have to go to white plains for that) but you can pick up necessities without going very far.
-It is cheaper than other towns (but more about that later).
-It is more "artist friendly" than other towns (again, more about that later.)
-The Peekskill coffee house is great, and there are some nice little restaurants.
-It is up and coming. Hopefully, in five years it will be alot nicer. There are alot of plans in place including a more thriving artist district and more leasing to mid-size employers.
-The Facts of Life was supposedly to take place there.
Cons-
-It's Peekskill. While there are definetly some nice developments going on (have you checked out riverbend yet?) and cute areas, Peekskill still has somewhat of a stigma in the socially conscious Westchester world. If people haven't spent alot of time there, they just think of it as some forgotton run down town in the upper corner of Westchester. But if you don't mind a couple of "oh..Peekskill...I see" from yuppies (which I certainly don't) then don't even worry about it.
-There ARE drugs deals going on at all hours of the day and night. You can turn a blind eye to it, but they are there.
-While there are SOME good things going on to make it "better" like more restaurants and such, Peekskill is REALLY lacking a decent nightlife. There are a couple of places to go, but they pretty much book the same bands all the time. And there is virtually no good nightlife close by either. You will have to go down county to find a more happening scene. If your not into going out on the town this shouldn't be a problem.
-While Peekskill IS in fact lower cost housing than other towns....not by much. Even Peekskill is showing the signs of a SERIOUSLY OVERPRICED housing market.
-From what I hear the school system sucks. But since you mentioned you have no kids...this shouldn't be a problem.
-While Peekskill is TRYING to become the Soho of Westchester....it's still got a LONG way to go. What's happening is this: Artists can't afford the rent. It's that simple. The lofts that they advertise go for AT LEAST $1500 per month and most $2000 and upwards. Only corporate people can afford that kind of rent, and if your corporate why would you want to live in Peekskill when you can afford the more expensive Yorktown or Somers which is closer to major employers. The artist lifestyle is very hard indeed, but Westchester County (even Peekskill) makes it impossible to afford to live there. So the whole artist thing isn't as good as it could be, and is a much slower go then they had planned.
-While Peekskill does have it's charm it still looks somewhat run down. They have done nothing....or very little to beautify the city, and it can look rather depressing at times. If they fixed up some store fronts a little bit and planted some green here and there it may have more of a pull.
-There are NO JOBS up there. Unless you are a social worker or healthcare person, good luck. With rising gas prices, and a ****ty commute on the Taconic to White Plains, plan on commuting to your job.
Bottom Line:
I like Peekskill, and I would consider living there myself. It really comes down to what your preferences are. Good Luck.