San Juan is wonderful to explore on foot. As Sandy mentioned, there are incredible forts, including El Morro and San Cristobal. A stroll down the promenade (Paseo la Princera) is lovely. Old San Juan is part of the U.S. National Park Service (designated a National Historic Site), and you can find more information here: San Juan National Historic Site - Places To Go (U.S. National Park Service)
. I've been to San Juan several times and have gone to the beach only once.