Juli, Juli, Juli, (sorry, and if that doesn't ring a bell, please ignore.) Yes, there is a museum of sorts, the Honolulu Police Museum at 801 South Beretania Street Honolulu, HI 96813. Though small, there is a portion of the museum dedicated to Chang Apana, the real life counterpart for the fictional detective: http://www.hawaii-vacation-fun.com/honolulu-police-museum.html
However, you might also check out one of the most famous tributes to the detective and his creator, Ohio Author Earl Derr Biggers at the newly opened "Earls", beachside bar. It lies within Halekulani Hotels' seaside restaurant "The House Without A Key", appropriately named after the first Chan novel. Read all about it here: