I went there solo for two weeks a few years ago. It was a great experience.
Having a rental car is super helpful. I found a great deal through
Costco Travel that beat anything else I saw. It was less than $50 a day I think. I slept in it a few times cuz I was on the cheap.
Check out Waikiki just to see it, but the beach is super busy and the mall shopping is for rich people. (Check out the big mall's little Japanese section though, it's a taste of Tokyo.) There is also a really cool little artificial lagoon to enjoy behind the Hilton Hawaiian Village hotel.
Pearl Harbor and its sunken ship memorial is a good historical stop. Diamond Head is a mildly taxing hike with a great view at the end. Set out early for both, the latter to avoid midday heat. Pill Box hike is solid too, more of a forested hill climb. Bring water.
Snorkeling is fantastic. Rent a snorkel, mask, fins from a shop, I found a good one in the southeast corner of Waikiki. Then you'll have that to bust out whenever you want to. Also, the shop I went to had vision-correcting masks, so I got one close to my glasses prescription. It ended up very inexpensive for the almost two weeks I carried them around.
Hanauma Bay is a beautiful place to get your feet wet, literally. If you drive there, be aware the parking lot often fills up. You might want to go early. If the lifeguards don't stop you you can swim out past the shallow coral to see huge schools of fish in deeper water. Listen to your safety instincts but try not to dwell too much on the fact that sharks exist, it can feel freaky being all exposed in open water.
If you're feeling more adventurous on the snorkeling front look up Electric Beach, kind of an unofficial bit of beach that has pristine waters to check out. (Some big rocks at the shore though, be careful going in and out.)
Try scuba! I had a fantastic first-time experience with Captain Greg of
Big Kahuna Water Sports. Super cool guy. I'll never forget, he and I had lunch afterward and at some point he was like, "Oh, did you hear? Apparently David Bowie died." That's how I found out. A blow to my soul.
On the east side of the island there is a little town (edit: it's Kailua) that has beautiful mini-islands offshore that, when it's not too windy, you can paddle a rental canoe out to. I set out too late in the morning to make the full trek out to the nicest islands, but it was still a really cool experience. Hit the water early and take a lunch!
In the north, toward the northeast, is a nice fancy hotel resort I walked right up to, enjoying its beach alongside the guests. It has a huge, free-seeming parking lot.
It can be neat to check out the sunset by driving up to a beach on the west side but be mindful that a lot of locals there aren't necessarily fond of tourists. Be ready for mosquito swarms, too.
Sample shave ice at various famous vendors. Try Hawaiian cuisine at a well-regarded hole in the wall. Try poke.
I can dig up the snorkel/canoe rental places I used if you're interested, lmk. They were both very good.
Infodump over.
