Next, I'll open Mailbox to check the emails I missed overnight. Mailbox is awesome because it helps me me get my inbox down to zero. I can even set a specific time for an email to pop to the top of my inbox.
Price:Free (mailbox isn't available yet but you can sign up to reserve it)
Before I roll out of bed I scroll through Tweetbot to see if I missed any interesting news overnight. Tweetbot is the best iPhone Twitter client around.