Allen:
My "back" faces north. That's where my lanai is. In warm weather, I love sitting on the lanai with my breakfast coffee and newspaper. In the heat of the summer, I may avoid the lanai in the late afternoon because part of it is directly exposed to the afternoon sun!
I worked quite hard to avoid a full western exposure. While searching for a place to which to move, I visited Plantation, south of Leesburg. Their model homes at the time all had lanais exposed to the late afternoon sun. They were unbearably hot!
My house "up north," had a southern exposure. We loved that our master bedroom was heated by the sun, and the sitting-room portion of it was our favorite venue. Here, my house does have a southern exposure, but it is mostly away from a place of activity!
Suggestion: bear in mind what you really like. If you want morning sun to ease your entrance into the day, consider an easterly-facing breakfast nook and/or lanai. If you like to sit with a glass of wine enjoying the late afternoon's ambience, consider a northerly-facing lanai, especially if a wall of it faces west.
As in all things, it's your personal choice that really, really matters!
SWR