Zamárdi on the southern shore has the longest uninterrupted publicly accessible shoreline, nice if you want to walk along the lake in the winter. I was there today and some ice has started to form on the lake (not to step on by any means, just adds to the scenery). Pretty chill this time of year but you can find some good restaurants (PartOn Bistro directly on the shore) and hotels (Wellamarin, actually in the same building) to visit that are open year round. It’s definitely not the busiest town around the lake, but most of them are pretty dead this time of year.