Tihany has three interesting ruins, so this city could be the ruin raiders' Mecca. The cave homes (Barátlakások) are definitely worth a tour.
You can park your car at the end of Árpád utca for free, and you'll reach the caves from the 10th-11th century through a path in half an hour. An interesting fact is that this is Central Europe's only, relatively intact hermit settlement.
You can get a good look on everything from the walk path: the lakes, the sailboats, the abbey's towers and the town. The silent forest, the butterflies and the songs of cicadas further enhance the calm and peaceful atmosphere.