Any suggestions?
And to clarify, someplace you can easily fly to and don’t need a car to get to.
NY city, of course you’ll still need the cab into the city but I believe it’s only $35-$40.
Tokyo.
San Francisco.
You’ll need a shuttle or taxi to get into the city from the airport but the city is very walkable and trolley-able. A full day or half day tour would get you to places like Sausalito and Muir Woods (Giant Redwoods) as well as Pt. Reis National Park and Stinson beach. But if you choose to skip that, the city offers enough to see and do for a few full days on foot.
You don’t need a car in downtown Boston. You also don’t (didn’t?) need one in downtown New Orleans although it is still a little injured but open for tourism.
Just about any city.
This is Mr. Athena and I’s favorite way of vacationing - having to navigate unfamiliar city streets in a car is a hassle. I’d much rather fly in, stay in a hotel in the city center, and be able to walk to most places I want to go and take taxis/subways for anything else.
Heck, even when we drive, we often park the car at the hotel and walk/taxi everywhere.
Most of the older US cities – Boston, New York, Chicago, Washington DC, Philadelphia, San Francisco.
Heck, the first time I visited LA I came by bus, and didn’t rent a car. But be prepared to walk a lot if you do that.
A lot of cities in the West you’ll really need a car (or else shell out for taxis and the like). I think I’d want a car in Denver or Santa Fe or LA. But there’s plenty to see without a car o r even public transit in Seattle (plus you can ride the monorail).
My wife and I spent four days in Seattle without a car – between the monorail, the Metro, and a lot to see and do within walking distance of downtown hotels, there was absolutely no need for a car. We took a Metro bus to the Museum of Flight, but walked to everything else. Well, we took a ferry to Bainbridge Island – I guess we didn’t walk there.
Key West – fly to Miami, transfer to small plane to Key West.
From the airport, you would need to take a taxi to your hotel. From there, you can walk pretty much anywhere you want to go.
How about Mackinac Island, MI? They have banned motorized vehicles for more than a century… Bicycles and horses (and foot) are the methods of travel there…
Disney World. They have buses from the airport to the hotels, and from the hotels to all the parks.
And if you stay at one of the Disney resorts, the shuttle from the airport is free.
I’m shocked that I’m the first person here to mention Las Vegas. You can fly in and take a free shuttle to wherever you’re staying, and then walk or take trams or buses to any part of the Strip.
The only problem is if you’re like me and don’t go to Vegas to hang on the Strip. But I’m not like most Vegas tourists.
Martha’s Vineyard is beautiful and you take a ferry to get to it. A gorgeous Island, big enough for thorough investigation but small enough to tool around on mopeds 
You don’t even need a shuttle or taxi to travel between SFO and the city anymore. BART goes all the way down to the airport now. As long as you don’t mind hauling your luggage with you, you can ride from your terminal right up to Market.
If you’re in decent shape, you could walk clear across San Francisco, from Ocean Beach to the ballpark on San Francisco Bay. Hell, I’m not in decent shape, and I bet I could do it.
I visited Chicago about a month ago, and I got around fine. I took a cab once, when I was tipsy and lost, but otherwise the Red Line and my feet got me around just fine.
Avalon, CA, on Catalina island about 30 miles off the coast of LA. Not only do you not need a car there, it’s pretty much impossible to get a car there (most of the locals use golf carts to putt around Avalon.)
Oahu is very easy to get around. In fact, I’d advise anyone vacationing in Waikiki not to rent a car. City busses (The Bus) are cheap and convenient and go to all of the tourist sites. In fact, when I moved there, I had a bit of an ethical dilemma since I couldn’t see charging people $20 for a tour of the Arizona Memorial at Pearl Harbor since the memorial itself is free and round trip bus fare was only $1.20 (prices have gone up since then).
Washington D.C. is another good place to vacation without a car. A Metro pass is $5.00 on the weekends and lets you ride all day.
If you’re interested in travelling abroad, London’s great. If you fly into Gatwick, you can catch a train straight from the airport to Victoria Station in the middle of London and take the Underground, busses or taxis from there.
I was going to mention Mackinac Isle, but he specifically said that he had to not need a car to GET there, too. I’m pretty sure there aren’t any major airports near there.
(If you can get there, though, it’s gorgeous - only vehicles I ever saw were two small pick-ups which were parked behind another building and marked “maintenence.”)
Actually, you can get the subway from JFK now (there’s a service called AirTrain that connects to the A at Howard Beach and also somplace in Queens for about $5).
LaGuardia is served by buses (which I personally find less convenient than the subway but its not fatal and it doesn’t cost $40).
Cape May, NJ
Fire Island, NY