From late January to end Feb and June through to August are the busy times in Vietnam so expect prices to at least double, no rock bottom deals and book ahead if you want a decent place to stay in a location of your choice.
Time to explore what there is to do on Cat Ba island
First you may need some transport, you can hire a local guy with a bike or take a tour but its very easy to rent an automatic bike and drive yourself around the island. (some knowledge on riding a motorbike would be beneficial).
Every place seems to offer bikes for rent so pick one that has decent, clean bikes and negotiate a price, typically US$2 to 8 per day depending on season and demand.
Cat Ba is a reasonably small island and only has a few roads, which are very quiet. It would still benefit to get a map of the island just so you have some ides of where things are!
Many places to stay offer free basic maps with the roads and island highlights marked on them.
Here are a few of the main places