For a first timer to Europe I would strongly recommend London! British Airways have some fantastic "weekend" deals. Enjoy a show! Unless you speak French, Spanish or what ever - language does pose a problem for first timers - so you will have no problem in London. Once you get your feet wet you will have no problem in Paris, Barcelona, or even Albania! Have a wonderful time and return again.

For the short stay you are planning I would imagine most of the cost will be airfare. If you are coming from New York I imagine you will have plenty of choices of direct routes.

Personally, in your situation I would pick London but then I live here so I guess I am a tad biased. It's a great place for a long weekend, good for an introduction to Europe and the New York-London air route is very competetive so you should be able to pick up a good fare.

That said, London certainly isn't the cheapest city in Europe but it doesn't need to be costly if you don't want it to be.

What city have you always wanted to visit?

Here's a second for the Bonaparte in Paris.

Also consider the Hotel du Lys and the Monge (recommended many times).

I always recommend Paris to first-time visitors. That way, if you die before you get back to Europe you won't be disappointed.