Yes - do a circle Island tour. I hate organised tours but had the same full day in Tahiti thing so booked a half day tour. The one I did included lunch at the Paul Gaugin museum which was thankfully closed so Rocky took us (only myself and one couple) to a Polynesian owned restaurant with plastic chairs and a 5 star menu. Kinda cool eating caviar, poisson cry and sashimi while the other couple were chewing down on chicken and salad rolls in a tiny shop. Because the Gauguin was closed Rocky took us to his favourite part of Tahiti - the Ismuth - and at my request down to Teahapu/Chopes where I had my very first ever surfing lesson
Saw Lava tubes, waterfalls, blowholes, grottos including the one where Gaugin the syphilitic deviant used to bathe in the hope it cured his syphylis - it didn't. Also visited Marae's for an awesome lesson in Polynesian History and lots of discussion as most Polynesians are very keenly interested in genealogy and curious about yours. Being a "pure Australian" I found out the Polynesians consider Indigenous Australians cousins who "just haven't got in contact yet".
They also do a half day tour - personally if I do have the opportunity to revisit I would happily pay extra for a personal tour with Rocky.
You can also hire a car and DIY but I found I got a great day well worth the value and saw so much more than with a guidebook and hirecar.
Papeete Marche is Ok it's just another market albeit with pearls tattooists boutiques and vegetables all under one roof. The city of Papeete is pretty much Meh in my view