I have to make presumptions in answering your question. I'm presuming that by "best," you mean least busy. Based on that, I would advise early Friday. I have to say that even the weekends are quite manageable. It's a great museum, a crown jewel in Philadelphia.
I do know that the Barnes Foundation is closed on Mondays. I'm not absolutely sure but I was suspect that going in the morning after rush hour is the best way to go.
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