Budapest neighboring villages to visit

The artist "town" you heard about is probably Szentendre. But it's a town and not a village, and yes there will be tourists. Still, its easy to get to and if before October you can take the commuter train up and the boat taxi back. I like entering Budapest by boat. Easy half day trip. Another option might be Vac, again more of a town than a village but very pretty and fewer tourists. It's a 30 minute train ride. North of Budapest the landscape is pretty and there are a number of interesting small village. I have heard by name of Pomáz and Kismaros and Fót and Zebegény; but to be honest I have never been there. But you have inspired me and in September I think I will get a car and go hunting. I suggest you contact a gentleman and a guide that I have known for nearly a decade now. Andrew ILLES can probably show you exactly what you are looking for. http://www.guideinbudapest.com/ Let me know how it goes. Then again, if you want to see something and learn, there are places in Budapest you could go, never see a tourist and learn a lot.

I'm sure the "artist village" is Szentendre. The town itself is quite beautiful, but IMHO the most interesting sight is the Skanzen, a open air museum with rural architecture from all parts of Hungary, even from parts that were lost after WW1 and are now part of Slovakia or Romania, and of former minorities like the Danube Swabians. Here is the site of the Skanzen:
http://skanzen.hu/index.php

I liked Szentendre (and I agree that's the one you heard about), but it did indeed feel touristy. It was still a worthwhile day trip; particularly interesting was the tiny new synagogue, the first new one built in Hungary after WWII. But I enjoyed my day trip to Vac even more. The mummies under the main town square were fascinating (they were discovered during a renovation of the square), and the soup and the pizza I had in the restaurant right off the square were delicious. Vac also had a restored synagogue, and I was just about the only tourist there (on a Sunday). As a bonus, it's an even shorter ride from Budapest (if you take the correct train - see next paragraph). A side note, relevant to your interest of seeing the "countryside." There are three trains almost every hour from Budapest to Vac; an express along the Danube (taking about 25 minutes), a local along the Danube, and a local going inland (taking about 90 minutes). Going there, I thought I was on the river-line express, but I was actually on the inland local. I indeed did get to see the countryside. The most striking thing was how the people getting on the train looked different from the people in Budapest (or Vac). Rick mentioned that outside of Budapest, you can sometimes see Central Asian facial features; to my surprise, I did, even that close to the city. I don't know if any of the places along that train line are worth a stopover.