One of our favourite parks in Bangkok for cycling is Suan Rot Fai which is part of the bigger Chatuchak Park in northern Bangkok. Last weekend I took Nong Grace there again as she likes cycling around the park. It is not too difficult for us to get there as we took our bicycles on the Skytrain to BTS Mochit. This is free but best not to go during rush hour as it can get pretty crowded. We went on a Sunday morning which is the best time. It is open every day from 5 a.m. to 9 p.m. Though I don’t advise you to go there at night for safety reasons.