I've never stayed overnight in Burgenland (it's not that far from Vienna) so I'm not of much use in the lodging info category, but I've made regular visits to the area over the past decade.
My short list would include visits with Franz Weninger, Paul Achs, Claus Preisinger, and Gerhard Kracher. Gernot Heinrich too, since he's sort of the ringleader of the group. All are making great wines and are swell people too. Their English language skills are at least as good as mine and they all have a lot of experience drinking wine from places other than their own backyard so they can put the wine they produce in context with what's happening in the rest of the world.
The Austrian Wine Marketing Board has a fabulous website that contains more information than you would probably ever want to access, but if you do, here's a link:
http://www.austrianwine.com/
You might also want to consider a day trip to Steiermark to visit Tement and Sattlerhof. Or make it an overnight trip and stay at the Genusshotel Riegersberg:
http://www.hotel-riegersburg.at/ It's owned by Alois Gölles so there is an incredible selection of distallates on hand. Beautiful hotel, great setting, worth the detour. Nice view of the castle too, and conveniently close to the local chocolate producer.
-Eden (and if you do get to the south and it's a hot day, it's a perfect setting to enjoy a glass of Schilcher, a wine that might confound even the hippest of the hipster sommeliers)
