Burgundy can be reached by train to Dijon from Paris, Brugges from Brussels by train. Alsace ..a high speed train from Paris to Strasbourg..

I'd base my landing airport somewhere between Zurich, Paris and Schipol. Alsace and the Belgian bits are nicely traped in that tirangle.

Burgundy is a big place. But head south west from Alsace and see if Chablis does it for you, if so keep going.

Schipol is the most useful hub for cheapo airlines on the mainland

How many days will you have to explore upon arrival from the U.S. before heading to Budapest? Are you going to be relying solely on public transport or will you have a rental car, or some combination of both? Also, provide specific dates for your arrival from and departure to the U.S. and how many of those days will be devoted to Budapest. The more specific you are the better the advice you'll receive.

I was a bit confused by your post but I understood you'll be flying in from the U.S., visiting some combination of Bruges/Ghent/Alsace/Burgundy and then continuing on to Budapest. I assume you'll be flying back to the U.S. after Budapest.

Yes, we will be flying in from the U.S. and visiting the combo of Bruges/Ghent/Alsace/Burgandy and then on to Budapest but will have to take the Euro Airlines back to our original arrival City from Budapest in order to get home.

Now we are looking at landing in Paris since that seems to be a more central location than Brussels.

Thank you all for your suggestions. We will have from the 30th of October until Nov 4th before heading to Budapest for the business.