If you want something special in the way of a heuriger, try Weingut am Reisenberg:
If you are willing to go a bit farther, Nierscher hits all the right notes with a lovely garden, the best heuriger food I have had anywhere, and nice people. Just take a taxi from Heiligenstadt. Once you get there you won't mind the extra cost.
I also highly recommend making the heurigen experience a full day one, rather than an evening. My favorite thing to do is to take the 38A bus from Heiligenstadt to Kahlenberg for the view of Vienna. Then take Stadtwanderweg 1 (a very walkable path through woods and vineyards which is very well marked) back down to Nussdorf. There are several outdoor heurigen (really called Buschenschank) which you will pass on the way down. Have a piece of bread with some freshly sliced ham and freshly grated horseradish on top with a glass of wine and you are set.
Slightly off topic, I have to disagree with Fred on staying in the Westbahnhof area. It is one of the few areas of Vienna I would term "seedy," especially the hotels along the main road (Gurtel). Lots of red light activity, graffiti, and general ugliness, in my opinion. Transportation is good from anywhere in Vienna, not just at Westbahnhof. I always wonder what kind of impression tourists get of Vienna when they stay in that area and wander around....
If someone if trying to avoid the cost of staying within the Ring, would suggest looking in districts 3, 4, and 8 (as close to the Ring as possible).
Wieden Bräu is great and I highly second that recommendation. Best pretzels I have ever had. Fred, you are correct that it is in a different district as Westbahnhof - Wieden is actually the proper name of the 4th District.
Fred, if you ever need to figure out how to get from one place to another in Vienna, you should use this link:
In addition, you could download the Qando app on your phone or tablet. This is the official app of the Wiener Linien and will help you get around town when visiting.