Pronounced closer to Tihan than to Tihany.
The small working abbey and royal crypt is worth the visit. The abbey historical displays are very well done, and you can easily spend 90 minutes in the place. Longer possibly.
The largest revelations I had on the tour concern the 11th century King Andrew I who ruled from 1046 to 1060. He is buried in the basement. He married Anastasia, a daughter of the king of Kyivan Rus and they had several kids. One would become king of Hungary, and one would become a Duchess of Bohemia. So, I got curious and did a bit more digging. Apparently, Norway, Denmark, Sweden, Hungary (several), France, Poland, Bulgaria, the Holly Roman Empire, the Ottoman Empire and Byzantium had Kyivan Rus queens at one time or another. The most well known married Henery I of France and gave birth to the future king Philip I. In French history, Henery and Philip are fairly big deals. Fascinating. Why would Western Europe travel so far for a queen? More reading some day.
It’s a great town with lots of arts and craft shops and little restaurants and views of the lake. A great day. The problem with Tihany is getting to it. By train and bus it can take 3 hours. Best done with a car. So I hired a car. I know a guy that I can afford. He was great as always.
At the highest point in town, with an unobstructed view of the lake is a restaurant called Echo. Yes, it’s a tourist place, but most tourists here are Hungarian so its Hungarian local too. The food and service is excellent.
Well worth a day trip. With a car I suggest you allow for not less than 7 hours and 8 is maybe better.