They call it ‘trekking’ in Bali, and it’s one of the best ways to explore. There are plenty of walking tracks around Ubud, and all tracks lead to rice fields. If you would like to spend a lot of time exploring the Ubud area by foot, I would highly recommend the Bali Pathfinder Map (which you can buy from book stores in Ubud for about $5). I also found a lot of useful information in blog posts by other travellers.
Campuhan Ridge was the walk I most enjoyed on both our trips to Ubud. I loved it for its beautiful scenery, and the tasty places to stop and eat on the way. I was also very taken by the idea that this is where lovers in Ubud go for some romantic alone time, and we were actually lucky enough on our last trip to see a local couple meeting here in their beautiful wedding clothes, before their ceremony.
Directions: Walk from Jalan Raya Ubud towards Penestanan. Just before the Temple, at the sign to Hotel Ibah on the right side of the road, turn right up the driveway to the hotel and then right again up a narrow walled pathway. Careful, there could be motorcycles coming down from the ridge in the opposite direction quite quickly.