Need to get from Györ to Hévìz and back to Györ by train and bus. How do I do this?
You have a few options:
a) take direct bus to Heviz, there are a few per day (for instance 5:45-8:33 or 13:05-15:57), it's fastest way to get from Gyor to Heviz. Bus ticket should cost 2520 HUF. Although remember that traveling by bus during winter might be not as reliable as doing using trains.
b) take a train from Gyor to Keszthely (nearest to Heviz town with rail connection). Journey will be longer (3-4 hours only to Keszthely) and require at least one change, ticket from Gyor-Keszthely start from 2830 HUF (one-way) + another 300 HUF for short bus trip (15-20 min.) from Keszthely to Heviz
Regarding potential issue with holiday time, Dec. 23 & 26 usually aren't the days when transport get canceled/don't run, so wouldn't worry about this, however if you do decide to use direct buses, then there might be a bit of a problem to get tickets, especially before departure. while with trains it's easier, since they don't get sold out and tickets are always available