Me and several friends will be in Budapest from Oct. 10-16 and are considering some unusual, non-touristy (or perhaps touristy) outdoor activities such as hiking, visiting natural areas, seeing wilderness, unique geological formations, etc. We are considering the cave tours beneath Budapest and will likely see several of the parks within the City, but are wondering if there's anything else reasonably close-by (day trip) with great views or natural experiences. Or if anyone has any other thoughts on interesting day trips, please let me know. Thanks!
I'll put in another one of my plugs for a day trip to Vac, a town on the Danube bend that (at least in 2008) was much less visited than Szentendre, but very interesting. The mummies found under the main square when they restored it were fascinating, as was the synagogue, and I had a great meal near the main square too (the restaurant was built into the area excavated under the square during its renovation). It's only 25 minutes from Budapest, if you take the correct train. There's an express along the Danube taking 25 minutes, a local along the Danube taking 45 minutes, and a local on an inland route taking 90 minutes. Guess which one I thought I was on, and guess which one I actually ended up on (at least on the way there; for the way back I got it sorted correctly).
Vac is not covered by Rick Steves; I learned about it from Frommers Budapest.
The cave tours as you mentioned: http://caving.hu/
Margaret Island: http://welovebudapest.com/budapest.and.hungary/sights.1/margaret.island
Janos Hill: http://welovebudapest.com/budapest.and.hungary/sights.1/janos.hill.janos.hegy
Kayaking on the Danube: http://www.evezzvelem.hu/canoeing-kayaking-daytrips-around-Budapest.php
Drive a Russian Tank: http://tank.hu/
The Bukk National Park: http://www.ieger.com/bukk-national-park.html
Budapest Chair Lift: http://welovebudapest.com/budapest.and.hungary/sights.1/zugliget.chairlift