Before arriving in Ubud, I had preconceived notions of what the the town would look like (thanks in part to what I had seen in Eat, Pray, Love.. I know, it's awful; guilty as charged). My point being that I imagined a town full of rice paddies and rainforests filled with beautiful villas at every corner. While Ubud and it's surrounding area do have these elements in spades, it isn't the whole story. Ubud itself is quite touristy, with most activities and shops catering around the main tourist drag along Jalan Raya. If you're looking for the Ubud you typically see in pictures and movies, you have to go out of your way to find it (usually by car or via tours).
Luckily, there is one less touristy escape in the heart of Ubud town: the Campuhan Ridge Walk. The ridge walk is a free, easily accessible trek that passes between two deep river valleys on either side. The trail, which starts right off the main road in town, takes you through patches of high grass, farms, small towns and, of course, rice paddies.
The full walk spans about 5.5 miles (in a complete loop starting and ending in town) but most people opt to only do the first 1-2 miles (up to Karsa Spa and back, see map and direction here), as this part of the trail is clear and well signed.
Whether you have the whole day to wander the countryside or just a few hours to see it's highlights, the Campuhan Ridge Walk is a must-do while in Ubud.