Least costly city to travel into Europe from the US ????

From the Midwest, I've found that London and Frankfurt are usually the cheapest. Dublin can also be very reasonable, as can Amsterdam. Check out www.kayak.com and www.farecompare.com to see what's cheapest from your area, and sign up on farecompare.com to receive alerts whenever your fares drop.

I would not be so concerned with the cost of airfare but rather the costs once you hit the ground. For example, London can be one of the cheapest cities to fly into, but your savings will be eaten up by staying there for two days. Italy or Greece will cost $100-$200 more to get to, but you will spend much less for hotels and food. One good destination, may be Amsterdam, relatively cheap to get to and can be done fairly low-cost.

Joe,
Paul makes good points. Ultimately your budget is affected by the entire trip. Often the flight is the least significant part (unless you really pay a high price).
Go to http://www.xe.com/ to see what the current currency exchange is. Then assume that everything costs the same in each country's currency as it does here. So a $20 meal will be €20 in countries who use the Euro and £20 in the UK. Do the exchange and that becomes $30 in Euro-land and $40 in the UK for the same meal.
Hotels are going to be similar. Areas such as Rome and Venice are around €100/night for a 2-3 star hotel plus or minus.
In the General Europe forum, there's a pretty lengthy thread on tips to save money. But ultimately, the flight, if going to Europe, isn't going to be where you'll save the most.
I recommend going to kayak.com and setting up a profile with several European destinations that will come with fare alerts via email. It'll give you a feel for air costs.

Joe, what do you want to do in Europe, other than fly to it? Do you then want to focus just on that very city you're flying in to? Or do you want to tour around? How many days of traveling were you thinking of? And what is it that you're actually interested in? Arts, architecture, culture (if so, which one?), party, shopping, nature...?

In recent years, flying with Northwest airlines from Detroit to Frankfurt in Germany has been one of the lowest priced ways to fly to Europe. And Germany is a great destination. I think you will find relatively low prices for flying to Frankfurt in April.

Joe, if you're talking about flying onto the continent, I have always found Frankfurt to be the least expensive European destination, and rental cars are inexpensive there, too.

Frankfurt and sometimes there are good deals to Zurich (like right now)London tacks on xtra fees for environmental taxes no longer the deal it used to be.

Once you fly into a cheap city it does not mean you have to stay there, if you pack lightly and don't mind a trip to another smaller aiport, you can often score a great deal on a cheap flight to where you really want to go