I would recommend a tour of an ukulele factory. KoAloha is the closest to Waikiki - across from the Ala Moana Mall at 1234 Kona Street, but Kamaka is not too far either, near the Kaka’ako area on South Street (the 19, 20 and 42 buses stop nearby). If you have a car or want a lovely bus ride to the Windward side of the island, Kanile’a is in Kaneohe.
To buy a uke, nothing beats The Ukulele Site’s store on the North Shore, Hawaii Music Supply.
As for live music, I would recommend the KaniKaPila Grille at the Outrigger on the Beach hotel in Waikiki.