There is an interesting group of temples in and around the area between the river and Thung Si Muang Park that can be covered in one pedicab trip (cost about 250 baht) in the following order: Wat Si Ubon Rattanaram, Wat Supattanaram, Wat Luang, Wat Klang, Wat Tai Phra Chao Yai Ong Tue, Wat Liab, Wat Burapha, and Wat Thung Si Muang. Two well-known temples, Wat Phra That Nong Bua and Wat Ban Na Muang, are on the outskirts of the city and can be reached by song-taew, as can Wat Nong Pah Pong, the former temple of well known forest monk, Ajahn Chah.
See the map in the Ubon Ratchathani guide.