Tourists are only now 'waking up to' the fact [=are only now starting to realize] that this is a great place to visit.
I spent every 'waking hour/moment' [=every hour/moment when I was awake] thinking about how to fix the problem.
She can never remember her dreams upon 'waking'.
(..) Come to my place to clean yourself. Over here. Madam... Shhh... Mrs Ianosi... Can't you see that you are waking up all the HQ? Let's go upstairs. And when they bombed the castle... My mood did not worsen at all. I kept laughing on and on. They thought i was crazy. (..)1965 Forest of the Hanged