Explore the island by motorbike
The best way to truly see Cat Ba island is on the back of a motorbike. If you know how to ride one, lucky you! Otherwise find a companion or hire a driver on basically any street corner. The island is way too big and hilly to explore on foot or bicycle and there is so much to see.
Three temples dedicated to each of the fabled women that Cat Ba island is named after are up in the hills with stunning views. There is a lookout point at Fort Canon with lots of secret bunkers from the war. A butterfly farm, a zoo, and lots of local culture can also be observed by meandering through the hillside. My favorite place I went to on the island is the Hospital Cave near the National Park. If you go just before sunset the light is absolutely beautiful.
Laze at one of the beaches
The beaches on Cat Ba island are surprisingly gorgeous. However, they are tiny and I imagine during the high season are positively crammed with tourists. Two of the beaches are backed by huge resorts which were all but empty when I was there (October) despite the perfect weather. Cat Ba 2 is most popular with backpackers as it has only a few small bungalows.
Hike at the National Park
Much of Cat Ba island is protected, thankfully, by a stunning National Park. The park has exotic species of animals, including the highly endangered golden headed langur, however spotting animals is uncommon. Cat Ba Adventure Tours and Blue Swimmer offer overnight hikes. There are other short, well marked trails that you can explore on your own and admission is less than one dollar.
Tour Ha Long Bay or Lan Ha Bay
The main attraction for anyone coming to Cat Ba island is access to the stunning limestone karsts in Ha Long and Lan Ha Bay. There are plenty of tours leaving every day with lots of variety, but be aware many of these tours are very low quality. I paid $20 for an all day tour of Lan Ha Bay with a visit to a cave, lunch, and kayaking, which was a ton of fun. I was in one of the most beautiful places on earth aboard a ship, what could be so bad about that? Nothing, but be aware that the guide barely spoke English and did not fulfill many things passengers were promised. I was sold a kayaking tour, we only kayaked for one hour with no guide. Another couple was sold a trip to Monkey Island, we never went there. Everyone was told we would stop at a remote beach. He took us to one covered by water in high tide. Blue Swimmer and Cat Ba Adventure Tours are said to have excellent, albeit more expensive, options.
Cat Ba Adventure Tours leads rock climbing expeditions which are said to be amazing. Given the scenery I can only imagine.
Kayak around the island
It is possible to rent kayaks for the day ($12) from Blue Swimmer and wander on your own. I wish I had done this perhaps instead of my tour to Lan Ha Bay to have a more authentic experience exploring the fish farms and local boats.