During my trip to Bolivia, I visited the province of Sur Lipez with an organised tour from Uyuni. I toured the region for 4 days in a 4x4. The first two days were dedicated to Salar and climbing Tunupa Volcano. The last two days were spent visiting the province of Sur Lipez.
The landscapes are radically different from those of Salar. I crossed several sandy deserts and stopped several times at the foot of volcanoes, such as Ollague and at numerous lagoons, such as the Red Lagoon and Laguna Verde. Dali Desert with the Arbol del Piedra (the Stone Tree) is fairly spectacular. You wonder how it's still there. The guide, Carlos, was really funny and nice. I was even able to bathe a little in a thermal bath, something which wasn't planned on the itinerary.