Per the suggestion of Vertical, my husband, mother-in-law and I visited one of the Family Fuhrgassl-Huber establishments (www.fuhlgassl-huber.at).
Vertical specifically recommended the Hauerkuchl which is not an orthodox Heuriger, however we checked the wine labels and the wine is made by the Fuhrgassl-Huber family. The perk to this type of establishment is that you have the convienence of a menu and it is much cheaper than the traditional buffet which can run 20 Euro+ per person for food alone.
The food and menu at Hauerkuchl was abundant and quite tasty. Our overall bill for three adults with food and wine was less than 50 Euro, though we did not go over the top. The outdoor dining garden is beautiful with lots of greenery and cat and a dog. Two musicians stopped by and played a few jolly songs, though they left early in our opinion. You can view their menu and prices on their website.
There were only two servers with many patrons to wait on, so service was non-existent. I was lucky to dine with my German husband so that I could read the menu and he could explain the dishes to me because the waitress was unwilling to do so. I would imagine this would be a difficult place for a non-German speaking person to dine at. Perhaps it was the busy time of day on a Friday evening that created this experience, but I would not advise my "English-only speaking" parents to attempt this restaurant without my husband.
The area is quite beautiful and you forget that you are so close to such a large city. The directions provided by Vertical were excellent as the bus stop is directly in front of the restaurant and the bus comes every 10 minutes.
(Directions from Vertical):
Neustift am Walde ( Bus 35A ) - no walking needed . The vineyards are just behind these heurigen and offer nice walks along the paths.
The 35A begins at the Spittlelau U-Bahn stop.
Where ever you decide to experience your first Heuriger - Enjoy!