As it turns out, the Perseid Meteor shower is still ongoing, giving us a second chance at the show Wednesday night if you missed it Tuesday night/Wednesday morning due to clouds (or just not enough caffeine).
This time, don't wait until after midnight -- I'd say any time after dark is good, so perhaps after 10 p.m.
(I was on the night shift Tuesday so I watched from Snohomish County when I got home around 12:45 am -- where it was still marginally clear -- and saw about 12-15 over the course of 30 minutes, including four really bright ones. Then the clouds rolled in from the south.)
But clouds are still around to muck up the viewing conditions tonight as well. The prospects for clearing skies are not great, but there should be some pockets here and there.
If you're willing to risk the clouds to go and see, find someplace dark. If you're in the greater metro Seattle area, you'll be best served getting out of the city. The site stardate.org had the good suggestion that it's dark enough if you can spot all the stars of the Little Dipper.
The mountains are a good place to go for darkness. I drove up to Snoqualmie Pass one year and found some field to watch. It's quite the show, but dress for warm and bring the coffee.
Once where you want to be, find a flat surface, lie down and look up. (I had to smirk at NASA's story where it suggests that picking the middle of a street for a flat viewing location is not a good idea. Um, I second that notion :) )
The meteors will be originating from near the Perseus constellation in the northeastern sky, but you can see a shooting star in any area of the sky. I found last night that best idea is just to pick one part of the sky and focus there because Murphy's Law says you'll miss them all if you keep shifting your head around. Again, being on your back is good as it gives you a larger view of the sky.