Shenyang has a metro system with several lines covering the main tourist areas. Line 1 connects Shenyang Station to the east of the city; Line 2 runs north-south and serves the airport and Beiling Park (for Zhaoling tomb). The metro is cheap, clean, and reasonably easy to navigate with a map.
Taxis are metered and inexpensive by international standards. Ride-hailing apps (Didi) work well in Shenyang. For the outer sights like Fuling Tomb, a taxi is more practical than public transport. The city centre around the Imperial Palace and Zhongjie is compact enough to walk.