Malatya City Museum is the most practical in-town museum stop when it is open, with exhibits on local history and prehistory. It matters because Malatya's story is easy to flatten into apricots and earthquake damage, when the region has been inhabited and contested for millennia.
Use it as background before going to Arslantepe or Battalgazi. The museum is central enough to fold into a walk, and it gives useful context without requiring a long visit.