Huay Keow waterfall and park is worth a look for an hour or two, park at the Buddha (Kruba Srivichai monument) just after the Zoo, walk through the flower shops and into the park.
Wang Bua Ban (3km further up the road) is a nice spot for a swim in a waterfall. After the parking spaces, walk down, turn left before the sala and carefully walk down the steep narrow trail for the best swimming hole.
Wat Umong underground shrine and fish feeding island another place worth exploring, just off Suthep road.