If there is only one museum in the town, I think, he works for the museum or he works at/in the museum is fine.
It doesn't matter how many museums there are in town. If there is only one museum, he can still work at the museum but not for the museum.
1. He works at the museum = his place of work is located inside the museum building.
2. He works in the museum = his place of work is located inside the museum building.
3. He words for the museum = the museum pays his wages/salary.
Numbers 1 and 2 can be true without 3 being true.
Number 3 can be true without numbers 1 or 2 being true.
1 and 3 together can be true.
2 and 3 together can be true.