Uyuni is a small grid you sleep in for a night either side of a tour, so the choice is really about noise, warmth and how far you are from the agencies.
Avenida Ferroviaria — beside the station
The strip running from the railway station towards Plaza Arce, where most tour agencies, hostels and bus offices sit within three blocks. Convenient for a morning pickup and a night bus, and the loudest part of town.
Around Plaza Arce — the quieter grid
Two or three blocks off the station the streets go residential and the noise drops, while still leaving a five-minute walk to the agencies. The better side of town if you have an early start.
Colchani and the salar edge
About 20km north on the road to the flat, where the salt-block hotels sit at the crust's edge. You get sunset and the night sky without a two-hour drive, but you need transport for everything and you pay several times town prices.
Ask about heating before you book
Uyuni sits at roughly 3,650m and nights drop below freezing for much of the year. Plenty of cheap rooms have no heating at all, so ask specifically about heating and hot water rather than assuming either.