Hi Kevin,
I went on business last November and only had a couple of hours in Central Park. I was in contact with Phil Jeffrey before who hopefully won't mind me posting his email here:
Subject: RE: Central Park birding
I recommend the small Eastern version of the Sibley/Audubon guide, particularly for sorting through the non-obvious sparrows. Sadly they aren't as striking as Chaffinch-Bullfinch-Greenfinch. (I'm an ex-pat Brit). We win with the warblers, however.
If you're a traveled UK birder the trip to Ellis Island and Liberty isn't going to add all that much, I suspect. Many of the waterbirds will be familiar. Great BB Gull and Herring Gull are the "same" depending on how you treat American Herring Gull. Ring-billed Gull is rather likely, but I think Laughing Gull would have moved on for the winter. Lesser BB Gull and the white-winged gulls are rare. The somewhat hardy Forster's Tern is possible, though very unlikely. On the duck and goose front there's a flock of Brant that plies NY Harbor, Canadas should be out in force, but Snow Geese are really only found in the Jamaica Bay area. Most of the ducks will be familiar, but the small black and white ones are more likely to be Bufflehead than Goldeneye. Most saltwater mergansers will be Red-breasted. Some chance at Hooded, but it and Common Merg/Goosander prefer freshwater. The latter really only comes down when the northern rivers freeze. Grebes would be Horned (Slavonian) and possibly Red-necked. Common Loon (GN Diver) and Red-throated Loons are distinctly possible. Probably more Double-crested than Great Cormorants at this stage - in particular with Double-crested look for the orange on the gape which can be pretty darn prominent. Great Cormorants are not very numerous around NYC.
I would take a quick look on the rocks for Purple Sandpiper. On Ellis Island the land birds may be: White-throated Sparrow, Song Sparrow, American Robin, House Finch, Northern Mockingbird, Northern Cardinal etc. "Suburban" birds. Maybe Yellow-rumped Warbler - by far the hardiest one.
At Battery Park - where you board the ferry, at least look around the grass briefly. Sometimes there's actually a Wild Turkey feeding there. Don't ask me why. Sometimes the Brant will feed on the lawn. The narrow strip of foliage etc that runs in the linear parks up the west side of Manhattan from here past the Jewish (Holocaust?) Museum can harbor wintering birds like White-throated Sparrow and give you a look over the water. Nothing epic expected, although there were vagrant hummingbirds here one year. Look up, also. There's a pair of Peregrines that nest on Water St and sometimes soar overhead. Also off a northerly wind, look up more. Sharp-shinned Hawk, Cooper's Hawk and potentially even Bald Eagle might fly over (Bald Eagle will put up every gull in sight off the water). The commonest Buzzard-shaped bird is Red-tailed Hawk. While numerous elsewhere, Turkey Vulture is uncommon to rare in NYC and Black Vulture is rare, but you might get a late straggler coming down from the north on a migratory wind.
In the park I'd concentrate on the Lake below the Ramble and then walk up through the Ramble, out of the Ramble to the Reservoir and loop down through the Pinetum to Tanner's Spring. This is a host of places you don't know, so look at:
http://www.nycbirds.com/mapCPK.html
On the Lake American Black Duck should be hanging out with Mallards. Familiar birds like Gadwall and N. Shoveler are possible. Green-winged Teal and Wood Duck are possibilities but unlikely. Don't spend much time here. Walk across somewhere like Bow Bridge and spend some time in the ramble. White-throated Sparrow should be easy to find, Song Sparrow not far behind it. For Chipping Sparrow and Dark-eyed Junco you're going to have to look in the more open grassy areas. Black-capped Chickadee is having an invasion year so likely to be present. N Cardinal, Downy and Red-bellied Woodpeckers, Tufted Titmouse, White-breasted Nuthatch, Common Grackle, American Robin, House Finch are all highly likely. One or both Kinglets, Brown Creeper, Yellow-bellied Sapsucker, Hermit Thrush are possible. There are feeders a little to the east of Azalea Pond in the place we call Evodia Field (that's literally 25 yards east of Azalea Pond - things really are named at that interval) that should pull some or all of these species in. From the Ramble head north and bird the south-WEST corner of the reservoir - because of prevailing westerlies this is the most likely place for ducks to aggregate. As well as your British dabblers, you stand a decent chance at: American Coot, Bufflehead, Ruddy Duck, Hooded Merganser, lots of gulls and there are still a good number of Cormorants around the general area. Canvasback and Lesser Scaup have sadly become rare here. Due south of the reservoir corner is a small patch of pines i.e the Pinetum that might net you Golden-crowned Kinglet, Sapsucker and Pine Warbler if your karma is really good. A little south of there (and really unobtrusive) is a small spring area that would bring in the common locals. And if you haven't seen a Common Grackle yet, you'd probably get one there. If you've already got Common Grackle you might dispense with it, although it does pull in migrants if you have time to stake it out.
For the tourist accompanying part, bear in mind that the Ramble is south-south-east (** treating Manhattan as N-S, which it's really not) of Delacorte Theatre, and the "castle" above it overlooks Turtle Pond. Potential water birds, sparrows skulking the weedy edges. The walk north-ish from here could take you directly to Tanner's Spring, Pinetum, Reservoir. When trying to find Tanner's Spring aim for the arch underneath the west park drive, then cut right up the grassy slope a bit and look for a small water-filled depressing with some fencing. It's "outside" the park drive loop, whereas all the other sites are inside it. The resident Red-tailed might be seen over the Ramble etc. There's also a pair that hunts north of the reservoir. On a hawk flight day Belvedere Castle is not the worst place to watch from (but Sharp-shinned can be difficult to separate from Cooper's, given that both look like Sparrowhawks and can come close in size). American Kestrel does breed nearby but isn't commonly seen in the park.
If you are spending any time around midtown I suggest looking at Bryant Park. Currently hosting a Prothonotary Warbler along 5th Ave end between 40th and 42nd - which is better than anything else you will find in NYC - it also holds YB Sapsucker and WT Sparrow. Check the rest of the park (between 5th and 6th) and you might find something else.
http://nycbirding.blogspot.com/2010/10/prothonotary-warbler-impersonates-house.html
Lists to check
NYSBirds via birdingonthe.net at:
http://birdingonthe.net/mailinglists/NYSB.html
eBirdsNYC at:
http://groups.yahoo.com/group/ebirdsnyc/messages
Hope this helps.