If you'd love to buy some original artwork at much higher quality than the crap at the 'art' markets, spend a morning at a couple of the cooperatives and galleries below. These are all south of Ubud, and I have suggested a couple of nice restaurants for your lunch within a few minutes drive of the Semar Kuning.
I also recommend you check out one of the Art Museums in town for an understanding of Balinese painting styles before you go searching for your own artwork to buy. See the museums link at the bottom of this article.
Tony Raka
I recommend starting here as the little cafe has great coffee. This is a modern Indonesian art gallery which is wonderful to browse and houses exhibits of new and established artists from all over Indonesia. This is a beautiful art 'space' and there are also workshops and music events.
Check their website for details.
Semar Kuning
This is a cooperative housing the works of over 120 living and past artists from Ubud and the surrounding areas. each section has slightly different painting styles from the modern to the ancient.
The more complex the work obviously its more expensive but you can also buy smaller pieces on a lower budget here, there's something for everyone (also start your negotiation at half the offering price).
Ubud Diary
Ubud Diary is a fun space with a curated collection of artwork for sale, in a predominantly Balinese and specifically Ubudian style. There are also wooden antiques and work from famous, now passed artists, plus a little cafe on what is a very pretty site. (open 9-5)
Lunch
Have lunch at Ubud Diary, or head to Ksuna Restaurant for something fancy. The Kayun Restaurant is in gorgeous surrounds and you can get an inexpensive and delicious Balinese style lunch. Semar Kuning Gallery has an associated restaurant but it's not very good. Bebek Tebesari is a beautiful spot where you can eat the Balinese favourite of fried or steamed duck.
Rudana Art Gallery
Back in town, next to the Rudana Museum, the gallery sells news pieces by up-and-coming Ubud artists.
Others
Titik Dua: This hotel has a great restaurant and is perfect for poolside brunch or cocktails. There is also a wonderful little gallery with regularly changing mostly modern Indonesian exhibitions.
Pilar Batu: If you are looking to splash out, this gallery on busy Jl. Made (opposite the petrol station) sells very high quality and beautiful new paintings from famous artists.
Komaneka: In central Ubud, Komaneka sells contemporary Indonesian art. It also has an art library and there are regular exhibitions.
Tanah Merah: A gorgeous collection of artwork and antiques for sale.
Kuluk Gallery: A curated selection of antiques and rare pieces from across Indonesia.
Titian Art Space (Biji World): Regular exhibitions from local and Indonesian-wide contemporary artists.