a walk in vienna woods

The Vienna Woods are more like a park on top of a hilltop in northwest Vienna. I've been there a few times since 1970. If I'm going out there, I'm riding a bus out. It's a pretty place at sunset, however.
Most people are going to the Vienna Woods to visit the wine gardens in Grinzing, eat dinner and listen to some oom-pah music. Some nights, it's a pretty lively place. Many prefer Nussdorf which has a number of popular restaurants, and it's due north. Kahlenberg is farther north than Nussdorf--up the river.
I would suggest you Google "Vienna Metro Maps" and find the bus/tram maps for the mass transit system of Vienna. Taxi's to go out to such a place might be very expensive.

I would highly recommend that you take the Vienna Heurigen Express - a small tourist train that leaves from Nussdorf, climbs the hill to Kahlenberg and then brings you back. You can hop on and hop off if the fancy strikes. Once you are finished with the train tour, have dinner at one of the three heurigen just opposite the train stop in Nussdorf (Scheubel-Auer is a good one).

Here is the link for the Vienna Heurigen Express, which provides schedule details:

http://www.wien.info/en/shopping-wining-dining/wine/heurigenexpress

To get to the station for this tourist train from your hotel, you should board Tram D which has numerous stops along the ring. Schottentor would be the closest to your hotel. Take the Tram D all the way to the end and get off. The Heurigen Express is just next to the stop. You would come back to the center of Vienna the same way - on Tram D.

I would also beg to differ with the characterization of the Vienna Woods as "a park on top of a hilltop", as mentioned above. It is actually a huge forest which extends for miles away from Vienna, roughly 45 by 30 kilometers in size. It includes towns, many hills and valleys.

Emily's suggestion sounds good. Also note that where Rick discusses the Vienna Woods transport in the Vienna book (p. 99 & 204), he says to take the U-4 (green) subway line to Heiligenstadt, then bus 38A to Kahlenberg or Leopoldsberg. I'm sure you'll get comfortable with the public transport system after a day in Vienna. You can connect to the U-4 at Schwedenplatz or Karlsplatz.

Bingo. Laura's public transit directions are exactly right. It is an easy connection.

Nice views (when the weather is clear) of Vienna and environs from the observation terrace by the church in Kahlenberg. Also a nice little cafe there. Once you get off at the Grinzing Line D tram stop, Bus 38A is about a 15-20 minute ride uphill through winding roads. Your tram/u-bahn ticket price includes the bus.