If you go to Uyuni you go there to see the saltflats. There is nothing else to do there.
Try to arrive there at night or in the early morning. The tours leave between 9 and 11am and you can book them on the same day in the morning. You can get them from 500bolivianos upwards for a 3 day tour with transfer to Chile to San Pedro de Atacama.
Get warm cloth, it is very cold there, especially at night, under 0degreese.
If you exit to Chile, get the exit stamp in Uyuni, you save a lot of time and maybe problems...