While it is not a national park, the Adirondack region of Upstate NY would fit. Perhaps the Catskills as well. You may like places close to the Adirondacks like Canton, Potsdam, Watertown, Plattsburgh, Utica, Rome, Gloversville, Saratoga Springs and Glens Falls, among others. Adirondacks, NY - Official ADK Region Tourism Site

The Adirondacks: Your Official Adirondack Mountains Guide To Hotels, Attractions, Real Estate, Vacation Guide & More!

The WILD Center | Where The Wild World of the Adirondacks Opens Before Your Eyes

Adirondack Region - NYS Parks, Recreation & Historic Preservation

http://www.iloveny.com/Cities-And-To...irondacks.aspx

The OP specified cities, so I'll limit my remarks to urban areas. Every city has hundreds, even thousands, of avid birdwatchers, who know of wonderful places for birdwatching inside the metro area. There are 194 species of birds that are seen every year in New York's Central Park, plus many other occasional sightings of other species.

Urban areas that are regularly visited by birdwatchers include San Diego, Tucson, McAllen TX, Duluth MN, Miami. All of those have many species that are difficult to find in other places. The urban density of birdwatchers means that any rare bird will be spotted by a local birder, but might have gone unnoticed in the middle of nowhere where nobody passes by who might have recognized it.

All American bidwatchers eventually wind up in St. Louis, the only place in North American where it is possible (in fact, easy) to see the Eurasian Tree Sparrow. Miami has a dozen or more species of parrots and parakeets, which originally came as escaped cage birds, and now form large, noisy flocks that are flourishing in the wild. At Niagara Falls in winter, you can see ten species of gulls in a day, plus a wide variety of wintering ducks and geese. Backyard bird feeders in Duluth are a haven to species that spend most of the year hidden in the inaccessible high arctic. The gardens in the metroplex of the lower Rio Grande valley attracts dozens of tropical species that that are hard to find elsewhere in the expanse of desert on either side of the border.

My guess is that you're not familiar with the natural bounty our area is blessed with.
If you haven't been, then I urge you to go to - The Everglades or any of our other national parks in South Florida. Go during the cooler months when its comfortable and wildlife is active and plentiful, particularly the birds. It's a great time to take the 15 mile bike loop through Shark Valley where you'll encounter deer, otters, snakes, alligators, and other animals up close. If you haven't taken a dive or snorkeled the reefs of John Pennekamp Park in Key Largo or the Keys then you've really missed out on wildlife experiences that you can only get(in the Continental USA) here in South Florida.

Don't listen to this homer. Florida sucks.

As others have suggested, upstate New York or New England may suit you better.

Or, if you want to change coasts, you could try Denver, some place in New Mexico, Flagstaff, AZ (very nice place), or pretty much anywhere from Northern Cali north along the coast.

Exactly - I was going to suggest Portland. We have eagles nesting in the city and large city, state and national parks/forests nearby.

Anchorage. If it isn't walking down your street, licking your car or getting into your trash, you can drive a few miles and find it.