Welcome to the forums Konstantin,
For a Balaton excursion I would suggest visiting the hilly north shore. The scenery is wonderful with panoramic views of the lake. Attractions that stand out include Balatonfüred, a charming bathing town, Tihany, a historic village known for its Benedictine Abbey (founded in 1055), the Baracsony Hill, one of Hungary’s great wine regions and Keszthely, a Baroque-style town with a castle dating back to 1745.
If you are looking to hit the beach, many of them are already open (they operate May through October). The water is warmer and shallower on the south shore and deeper and somewhat cooler on the north. There are popular beaches all around the lake. See our Balaton page for more info.
The best way to get to Lake Balaton is by train. Most trains depart from Déli Pályaudvar and the ride takes about three hours. Another option is to take a personalized tour with a local guide. MypersonalBudapest offers Lake Balaton day trips from Budapest, including wine tasting, sightseeing, meals and more. Tours can be customized to your wishes.
Hope this helps.
Enjoy your trip and let me know if you had any other questions.