The Comrat Regional History Museum is a useful first stop because it puts Gagauzia's culture into objects: textiles, domestic tools, handcrafts, photographs, and local historical material. English signage is limited, but the displays are still worth the small effort.
It is the kind of museum that works best when you slow down. Look at the clothes, carpets, and household pieces, then compare them with what you see in the villages and markets outside the city.