Kushinagar Museum is a small archaeological museum near the main pilgrimage zone. Its collection includes sculptures, fragments, and finds from the surrounding Buddhist sites, giving useful background to what can otherwise look like a series of brick mounds and modern temples.
The museum is not elaborate, and opening hours can be worth checking locally. Still, it helps connect Kushinagar to the wider Buddhist archaeology of the Ganges plain and is a sensible stop if you have more than a rushed hour in town.