The Pearl River Delta surrounds Guangzhou with easy connections to Hong Kong (50 minutes by high-speed rail), Macau (by ferry, about 1.5 hours), and Shenzhen (30 minutes by high-speed rail). These three destinations are the most natural day trips.
Within Guangdong province, the town of Foshan — historically famous for Cantonese opera and ceramic production — is 20 minutes by metro from central Guangzhou (the metro crosses into Foshan directly). The ancestral temple there, Zumiao, is one of the best-preserved Qing-era temple complexes in southern China.
The Danxia Mountain scenic area (Shaoguan prefecture) is a UNESCO World Heritage site of dramatic red sandstone formations about two hours north by high-speed rail — a full day excursion worth making if you have time.