The north shore is the wine-and-spa side and stays open longest, the south shore is the beach-and-clubs side and empties out of season, and the west end is the only part that behaves like a normal town in winter.
Balatonfüred — the north-shore default
Spa town with a railway station, a marina, the ferry pier and the widest choice of places still open in September. The easiest base if you are arriving by train and want to do the lake without a car.
Tihany — quiet nights, crowded days
The peninsula village above the abbey empties in the evening when the day-trippers take the ferry back, which is exactly when it is worth being there. Few beds, high prices, and a bus service that thins out badly off-season.
Siófok — the south shore, in season only
The beach and bar strip is where the lake's nightlife actually happens, and it is walkable and cheap outside July and August. Come in May or late September and much of it is shuttered.
Keszthely — the west end that stays open
A proper year-round town at the far end of the lake, with the Festetics palace, a station and Hévíz a short bus ride away. The sensible base if you are visiting between October and April.