At CAN, stay airside—Baiyun is sprawling and immigration plus transport time make short exits unrealistic.
Take Metro Line 3 from CAN to Tianhe Sports Center Station in about 45 minutes (CNY 10). The area around the station has shopping malls and restaurants. With TWOV clearance, this is practical for eligible passport holders. Allow 90 minutes total travel time and a 2-hour departure buffer, leaving roughly 60 to 90 minutes in the city. Stick to the Tianhe CBD area rather than crossing the city.
Shamian Island is 55 minutes from the airport by Metro Line 3 to Huangsha Station, then a short walk across the bridge. The island has preserved European colonial buildings, a riverside walkway, and cafes. Allow 90 minutes on the island. Zhujiang New Town (Tianhe, Metro Line 3) offers the modern side of Guangzhou: glass towers, riverfront, and the Guangdong Museum (free on weekdays). Budget CNY 60 to 100 ($9 to $14) for lunch.
Canton Tower (TV tower with observation deck, CNY 150) is 50 minutes from the airport by Metro Line 3 directly to Canton Tower Station. Baiyun Mountain is 30 minutes north of the city by taxi (CNY 30 to 40) and has hiking trails with city views. Combining Shamian Island in the morning with Zhujiang New Town for lunch and Canton Tower views in the afternoon is a strong 6 to 8 hour city circuit.