Yangshuo town itself is small enough to walk, but most of the things worth seeing are in the countryside outside it. Bicycle rental is the standard solution and works well: the valley roads are flat, the traffic is light compared to most Chinese towns, and you can reach Moon Hill, the Yulong River, and most of the countryside sights within 30 to 60 minutes of pedalling. Rental shops on West Street and around the bus station charge 30 to 50 yuan per day for a decent bike; electric bikes are available for slightly more.
Bamboo rafts are the other standard mode for covering the Yulong River section. You drift rather than paddle; a raft operator handles the poles. Combine a bicycle ride out with a raft ride back, or vice versa. Motorcycle taxis (sanluncia) handle the longer distances or the route out to the Impression Sanjie Liu theatre in the evening. Agree the price before departing.