Run, watch TV, browse the internet (You heard of Imgur? Funny stuff), work out, watch a movie, Netflix (A cheap 7.99 a month distraction), go for drive, got for a walk, call a friend, go to dinner, cook, bake, go to the movies with a friend or alone, go for a hike...basically do ANYTHING that you enjoy doing or that keeps you busy.
If it's early in the morning (5:30 here in Boston) try and get back to sleep by doing something silly like the ABC game, it sound stupid but it helps me shut down negative thoughts and fall back asleep. It didn't work for me today because I know I need to be up at 7:00 today and I'd rather just stay up but what I normally do is I pick a TV show I watch a lot like 30 Rock and I try and think of a character with a first or last name for every letter of the alphabet. Sounds lame but it's just a little trick I use to quiet my head and relax my thoughts and catch a few extra hours of sleep!
Back when I quit drinking the first time, after doing so every day heavily for MONTHS I had really bad drinking dreams ! I think it's 100 percent normal and always a relief when you wake up and realize you're still sober and not hung-over.
Congratulations on your recovery and sobriety and best of luck to you
(PS- I'm wicked lame and I watch Pretty Little Liars (I blame Netflix) and the name "Fitz" is the same name of a teacher who is sleeping with his student, lol, which the show acts like is totally normal and acceptable haha)