Indian summer and bike tours
In autumn, you can still often catch a sunny, nice weather, and you can still splash around in Lake Balaton. Of course, there are plenty of places to visit, either by boots or by bike: e.g. Tour to Kis-Balaton.
The wine cellars in the area are also worth a visit.
Hévíz is 8 km away, the Tapolca Spring Cave is 17 km away and the Csodabogyós Cave in Ederics is also 8 km away.