I have no words to describe Lamu. It's truly a special piece of paradise, but is quickly getting more and more popular - so go asap!
There are two main parts to Lamu that you should visit. One being Lamu Old Town and the other is Shela (the other side of the island).
Lamu Old Town, a UNESCO World Heritage site, is a living museum with narrow streets, ornate doorways, and beautiful coral stone buildings. It's where most of the locals live and is a really culturally rich place. Definitely worth a visit (maybe a few).
Shela is where a lot of expats have built huge beautiful Swahili style homes. It's also where the swimming beaches are. It's my favourite place to stay.
Where to stay:
There are a lot of houses to rent, all which can be found on Airbnb. I think this is the best place to book.
There is also a great hotel, a classic and a landmark of the little town - Peponi. It's very expensive but is amazing. Even if you aren't staying there, make sure to go for sundowners and sit on their terarce. The food is also great and they often have live music.
What to do:
SO MUCH!
First of all, just wandering Shela and Lamu Old Town is great.
Drinks at Peponi
Take a Dhow Ride on traditional old Dhow's at sunset
Snorkeling
Sailing
Stand Up paddle board
Walk along the really long beach from Shela
Visit the ruins
Go across the water to Manda (check out the Majilis or Diamond Beach Village)
Relax!