A famous and typical Kaffeehaus in Vienna is the Hawelka Cafe, not far from Stephansdom:http://www.hawelka.at/cafe/de/
In another style, but also very popular, the Cafe Centralhttp://www.palaisevents.at/en/cafecentral.html
My favorite is the Cafe Sperl (with pool tables), near the Naschmarkthttp://www.cafesperl.at/html/CSkap1.html
For Heurigen is the best choice Grinzing in the northwest of Vienna (tram 38, I think), there are a lot of wine taverns.
Since you were already in Vienna, you certainly know the main attractions. My recommendation would be the Post Office Savings Bank by Otto Wagner (it is open only on weekdays):http://www.ottowagner.com/home-en-us
or see my reviewhttp://www.worldheritagesite.org/sites/vienna.html
Neusiedlersee in January is not a good idea, but I can recommend a trip to Graz. It takes about 2.5 hours by train from Vienna. One day should be enough to visit Graz. A must is to climb the stairs on the Schloßberg. From there you have a beautiful view over the roofs of Graz and the modern Kunsthaus. The historic center is worth visiting. There are hardly any traditional Kaffeehäuser in Graz (unlike in Vienna), but plenty of pubs and restaurants in the center.
I wish you a nice trip