I work overnight shift, so the morning appts are what works best for me. Outcalls can potentially be a little difficult, but when I have tried I have been able to get a room in the morning as long as I check out by 2:00.
One of the hottest sessions I ever had was with a lady early in the morning 7:30am for 2hours. And we went at it for two hours almost without stopping. She was a hottie in the morning and I was really ready that morning. We took a nice shower before heading off on our regular day.
It was perfect because I could just tell work "I have a Dr. appt in the morning. I will be in around 10am." Of course I had a big grin all day long.
Depending how early you are talking - I am up an early bird. I'm usually up by around 7 or 8am. I am available earlier as long as I know by the night before.