As far as I know, they all do. Because of FATCA, requirements and expectations may be a bit higher and KYC a little stricter for US persons.
Just start sending emails and making phone calls. Some of them require an intermediary but for personal banking, they're often more lenient. You can start trying with Absa, Maubank, MCB, and SBM. I believe Bank One and AfrAsia also take customers directly, at least for personal banking.
By and large, banking in Mauritius is fine for small personal banking. Fees are usually reasonable and they are happy with relatively modest minimum deposits most of the time. MCB is an exception, requiring at least 500,000 USD for non-resident clients. IIRC, the rest just want a few thousand.