Kayak is a more broad site to look for flights,hotels, etc ..but I mainly use it to book car rentals around different countries.
Air b and b is a great way to book an accommodation with a local, I encourage you to read the reviews and loook at the location before booking =)
Hostelworld is the website I use when I want to search for a specific hostel (shared rooms with multiple beds, a cheaper option if you are on a budget)