You can find Sandspitters in the new Desert Wetlands biome, which can be found on desert planets. You can easily tell the biome apart by the abundance of quicksand. Not every instance of the biome will spawn Sandspitters, but he majority will, under normal circumstances.

It should be noted that having Frackin' Universe installed greatly decreases your odds of finding the biome, as FU adds a lot of additional sub-biomes to the pool. The wetlands biomes will still spawn occasionally, but not as frequently as without Frackin' Universe.

If you can't find the biome at all, or none of them spawn Sandspitters, you can head to the Starfarer's Refuge and purchase the quest items instead. You can find a black market shop - the Drifter's Emporium - in the upper sections of the Refuge, by heading into the overhead pipelines with a Distortion Sphere tech.