Reddit mentions of Mit Bahn und Bus in die Wiener Hausberge: 50 Touren zwischen Donau, Mur und Enns. Mit GPS-Daten

Seconding Stadtwanderwege that were already mentioned! For a smaller half-day or lazy day trip in Vienna's immediate surroundings, I would recommend Naturpark Föhrenberge including Perchtoldsdorfer Heide (really neat rock formtions and views down on Vienna, unique vegetation). Another good option would be Nationalpark Donauauen (flat, lots of water and birds and open space, also good for swimming). I'd also recommend you to end your trip at a Heuriger, a traditional restaurant run by wine producers, consider starting and ending your trip in Grinzing for that, the South-Western area around Baden is also good for that. Look for any hiking trip recommendation containing the word "Wein" (wine), hehe.

If you want something a bit more involved, like a full-day trip with proper mountains, and maybe a stay in mountain hut, I can also recommend the hiking trips in this book (Amazon link here); it countains trips like this (I can recommend this one by the way). Try translating it through Google Translate and DeepL, the latter sometimes gives better results. If you don't want to buy it just for a day, there's a list of all the tours it contains here, you could then look up the names of recommended areas for hiking trips on either www.bergfex.at, www.outdooractive.com or www.alpenvereinaktiv.com (also available as apps). Also check out the apps Komoot and Mapy.cz, and Osmand for good offline openstreetmaps (which are sometimes more detailed for hiking paths than GMaps).

There's lots of lists and material, but most of it is available in German, shouldn't give you too much of a problem though if you use any of those sources for ideas, and then look up the tracks on abovementioned websites. Don't rely on the indicated train connections, some of the sources are from last year and things might have changed (recommended websites for that: www.oebb.at, www.anachb.at, and as apps ÖBB or Wegfinder, the latter also for the city). Also make sure your phone is fully charged and your equipment is fitting for the planned trip (proper shoes, clothing for rain protection and warmth, emergency medical kit, maybe a small flashlight, tell people where you're headed) and above all, have fun!

Some more sources:

List on environmentally friendly = public transport trips to the "Wiener Hausberge", the "Vienna house mountains" or mountains closely around Vienna. Contains this nice pdf.

Some of the trips already mentioned as list on Komoot.

List of trips reachable by train.

Another book, don't have any experience with this one personally.

Oh and also check out www.viennawurstelstand.com for various general info about Vienna in English. Also contains some hiking trip ideas here and here. www.wien.info is good for general tourist infos.