Sam's right, it's usually book a hotel, then check into it. But a lot of people do say 'book into a hotel' - which means book in and check in all in one go! So, if you have plenty of time to plan - book your hotel then check in at the appointed time. If you're in a rush, grab your bags and book into a hotel now!

"To book a hotel" is to schedule a stay, e.g. "I booked a hotel for Wednesday night." I've never heard "To book into a hotel", but I'd imagine it's the same as "check into", unless that's what you meant in the first place - "to check into a hotel" is when you are at the hotel and get your hotel keys and stuff.