I plan on taking a day off from work to spend a whole day "attending" WWDC. Which day would be best? I'm thinking Wednesday or Thursday because a good amount of content would be posted by mid-week.

I would take the day off for The Keynote and State of the Union speech as everything is online and available to watch when every you want. While the Keynote/State of Union is recorded but you less likey to watch them after you will know everything that happens in them.

Then I usally also check tweets and Paul's has a "What to Watch" list. Watch these first.

However if you want to attend any of the lounges or watch a particular workshop then you would have to wait until they announce the schedules.