I'd splash out for a good breakfast at any of the better hotels in town - by the time I'd be ready, most everything is open.

Definitely leave the airport for town. As you said, you'd have net 7 hrs to spend there - you can fit a lot in there if so inclined (especially if you're first timer there)

As I go to BKK on a regular basis, I'd probably just head for the (let's say) Millenium Hilton, have the breakfast at their riverside restaurant, watch the life on the river, hit their spa (expensive for BKK, cheap for Scandinavians) and then go up to the pool area with a good book. Have a late lunch before heading back to the airport.