Tindouf is not a place tourists come to look at things. Almost everyone who passes through is on official business — diplomatic, journalistic, humanitarian, military — and the town's interest is largely sociological rather than scenic. That said, the small original old town survives in fragments behind the modern grid of administrative buildings, and the surrounding Sahrawi refugee camps are one of the longest-running displaced populations in the world and are accessible (with permission) to outside visitors.
The annual Mouggar de Tindouf is the one event for which the town fills up. It is a Saharan cultural festival drawing musicians, poets, dancers, and herders from across the western Sahara, and is the closest thing the place has to a tourist season. Beyond that, the appeal is the desert itself — the Hammada du Draa stone plateau that stretches west toward the Mauritanian border is one of the bleakest and most spectacular landscapes in the Sahara.
A reality check: Tindouf has been politically and militarily sensitive for fifty years. Foreigners must be registered with the authorities on arrival, photography of government buildings is restricted, and travel beyond the wilaya boundary requires explicit permission. Plan accordingly.