Brunei is a dry country: alcohol is not sold anywhere in the country and consumption of alcohol in public is prohibited by law. That said, non-Muslim visitors are allowed to bring in up to two litres of alcohol wine or spirits plus up to twelve cans of beer every 48 hours, and there is a wide array of duty-free shops just across the border in Malaysia to cater to this demand. However, alcohol permits must be obtained upon arrival in Brunei while going through customs.
Many higher-end restaurants allow guests to bring in their own alcohol and corkage is not charged, though this is technically illegal and it's best to keep a low profile if you choose to consume in a public establishment. At the lower end particularly Chinese restaurants, many restaurants supply illicit booze under euphemisms like "special tea".
One should definitely try out teh tarik, a sweet milk tea, as well as the wide array of coffee kopi available in restaurants.