Wuhan has one of the most extensive metro systems in China — more than 14 lines and over 500 kilometres of track, growing every year. The metro is the easy way around the city: trains run from roughly 6:00 to 23:00, fares are 2–7 RMB depending on distance, and English signage is good. Buy a stored-value card or use Alipay/WeChat to pay.
Taxis are abundant and cheap. Insist on the meter — most drivers in Wuhan are honest, but flagging an unmetered car at a tourist site is asking for trouble. Few drivers speak English; have your destination written in Chinese, or use the Didi app, which is the local Uber and has English language settings.
Ferries cross the Yangtze between Wuchang and Hankou for a few RMB; they are slower than the metro but worth taking once for the view of the city from the river. Bike-share schemes (Meituan, Hello) cover most of the centre.