1) We've done two bike tours, one starting near Bedugul, and one near Kintamani. Both end near Ubud, and take you through little villages on back roads, with the guide stopping to explain what you're seeing. Both routes are slightly downhill for the entire route, making the cycling very easy.
The first one, from near Bedugul, was enjoyable. The second one, starting at Kintamani, was
great, and I highly recommend it! The company is Bali Hai Bike Tours, here:
Bali Hai Bike Tours, Bali Adventure & Cycling Tours through Bali?s Unspoiled Countryside
Here is a Youtube video about their operation:
Bali Hai Bike Tours - YouTube
The equipment is very nice, the pace is relaxed, and you stop often to rest or learn about the local attraction. The traditional village they tour, Penglipuran, is quite beautiful, and the temple, Pura Kehen, was really interesting, and that's after having seen a good number of Balinese temples. The breakfast view looks out over the volcano Gunung Batur and the lake below it, and the afternoon meal (which is excellent) looks out over the ocean from a high point near Ubud. Some bike tours are cheaper, but the combination of meals, equipment, route, attractions, and length of time make this a hot ticket, IMHO.
2) Find a good guide/driver and tour the rice terraces at Jatiluwih and the temple Pura Luhur Batu Karu beyond it. This temple is well off the beaten path, and the drive getting there is worth it.
3) Just west of the crossroads in Ubud, start walking north up Jalan Kajeng, and just keep walking. You'll end up in beautiful rice fields, and continue walking a several kilometer counterclockwise loop right back to the middle of Ubud. Lots of locals, lots of smiles, and you're out of the craziness of the center of Ubud.
4) Spend a couple nights in a traditional wooden room (upstairs is better) at Tegal Sari in Ubud. You can sit on the porch and look out over the rice field, listening to the monkeys and gamelan music from the temple beyond it.
PM me for more; I also take donations for my Bali retirement fund.