Another vote for paying for the night before.
You can always get coffee and pastries and go to a museum after you find a place to stow your bags, but wouldn't you rather take a power nap, then get up refreshed and have the rest of the afternoon to explore without fighting sleep?
I started reserving the night before a couple of years ago after one too many miserable mornings, unable to enjoy whatever I was doing because I was so sleepy and just looking at my watch to see if it was 3:00 pm yet.
It's become a necessity, not a luxury. I'll cut costs somewhere else before I spend six or seven hours waiting to check in.