Where in Manhattan is your dinner? In some neighborhoods there are neighborhood car services that will pick you up on a moment's notice. In my 'hood, for example (the Lower East Side),
Delancey and
New Day both have cars that are generally available on-demand to go anywhere in the city for roughly the same price as a yellow cab (we use them all the time as it's easier to call them than to try to find a cab near my building). I wouldn't be surprised if they'd be willing to go to the 'burbs, too.
Even if you're not having dinner downtown, though, you might want to give New Day a ring, as they do a bit less neighborhood-around-town business and a bit more airport-type rides (and their cars on average are a notch nicer than Delancey's). I've used them for several airport rides myself, and I've had them pick my parents up at both LGA and HPN for rides to Dutchess County, NY, for example. All were scheduled, though.
Three warnings about expecting spur-of-the-moment pickups:
1) Both Delancey and New Day are very curt on the phone (as are many other car services in the city). Don't take it personally.
2) If it's particularly rainy or a big party night (Halloween, New Years, etc.) they often won't have cars available.
3) Expect to pay cash. Both can arrange for credit cards, but it's a pain in the butt and they'll charge a LOT more for it.