Start with Festetics Palace, the most complete aristocratic monument around Lake Balaton. The palace and park justify the stop even if you are not staying overnight.
After that, Keszthely becomes more relaxed: wander the centre, visit the Keszthely Synagogue, swim from the town beach, or make the short trip to Lake Hévíz. For a broader lake view, head east along the shore to Vonyarcvashegy and Balatongyörök.