For me I try to think of a few things:

1) Where will I cause the least damage. If it is say near a lake or on the PCT or at Mt. Rainier NP you often have no choice: you take the established campsite. After that I start thinking....

2) Look up, around and all over. Which way will the wind come at night? The trees above and rocks nearby.

3) In that area where will my tent fit best - when with others sharing an area we have to think this out.

Last but not least....I try to avoid alpine bowls - while pretty and great in early evening/late morning....they get cold and dew filled at night - especially with a cold wind pouring down a snow field all night across an alpine lake. Brrrrr.....

I also think about what would happen if a freak storm came in and make sure I am not too close to any water source.