from Vienna airport to Heviz

Making a journey from Vienna/Vienna Airport to Heviz unfortunately are not among the easiest trips, but we'll try to explain all the option you have:

a) get private/group transfer. It won't be cheap + reliability of such charter type transfers aren't great (in pm we sent you couple links for the companies that might help you out, but also we would really recommend emailing your hotel/guest house in Heviz and asking administrators about private transfer possibilities, it might be the best option)
b) most reliable way to travel using public transport is going via Budapest. Hungarian Eurolines bus company offers direct buses from Vienna Airport to Budapest for as low as 5900 HUF per person on Dec.27 (for instance departure 11:15am with arr. to Budapest at 13:55), then from the same bus station you can catch direct Hungarian domestic bus to Heviz (for instance 14:15-17:05, from 3700 HUF per person), tickets for both legs can be bought at eurolines.hu website. The convenient thing about such an itinerary is that you reach Heviz with only one change. The big minus here is that you travel all the way by bus. As an alternative the same route (Vienna-Budapest-Heviz) can be done mostly by train, but in this case it will be necessary to travel first from Vienna Airport to Vienna train station, then from there to Budapest, from Budapest to Keszthely (nearest to Heviz train station) and finally last 8 km from Keszthely to Heviz by local bus, which means 3 changes.
c) if you are up for an adventure and exploring rural areas, then it's possible to plan a trip without going via Budapest at all (if you look at the map Budapest is quite a detour from the most direct route). Instead the trip to Heviz can be done via Sopron-Szombathely or via Gyor-Keszthely, but in these cases you have to make a number of changes + not always ticket purchase in advance will be possible, thus you have to buy your ticket as you go. In case you interested - let us know and we can help out with exact schedules and fare info.