Nice hotel! I'm tempted to send you to Khao San Road where you can hang out with the tourists, but I'm wondering if it might be a bit too, uh, rustic for you. In your shoes I'd go to the hotel at night and have the concierge hold my bags until I check in. I'd then go to Khao San Road, explore and have a drink. If could keep myself occupied until five in the morning, I'd try to find a monastery or temple to see if any monks are stirring. If not, I'd arrange a room in one of the local guest houses for a pittance.
The hotel's restaurant opens really early so you could have a leisurely breakfast and hang out by the pool. Not far from the hotel there's a little side-street morning market that's quite busy in the pre-dawn hours. That's where I'd be hanging out.
The hotel is also the starting point of some tour companies. Call them to see which tour leaves the earliest; they're a bit pricey (in my opinion), but very well done.