Whether you're installing your own backyard tennis court or looking for the best place to play, the orientation of your court can have a huge impact on your service game. You may have noticed in your travels that most public tennis courts face north and south. This is the case because most tennis games are played in the morning or evening when the sun is fairly low in the sky. When oriented east and west one of the players would be constantly looking into the sun during the game, and for most players, the sun sits right where they serve the ball. If the courts you use for tournament play face east and west they will give one player an unfair advantage. The best courts will also avoid lining the tennis nets up with tall shady trees. Thus, there are two factors in tennis court design that must be accounted for: The sun and shadows cast on the court surface.
These may seem like minute problems, but if you are frustrated by the effects of these outside influences while playing, you aren't going to enjoy your tennis court.
So, north and south is the answer?
North and south orientation is mostly the answer. Because the earth doesn't spin straight up and down on its axis, but instead at a 23.5 degree tilt, you don't want to be true north and south. By arranging your tennis courts at 22 degrees from true north you will maximize the usability of your tennis courts year round. Instead, the sun will strike your tennis nets at a pleasant angle, away from either player's eyes.
But what about the shadows you mentioned?
The sun can do more than just shine in your player's eyes. If you build your courts where there are tall structures or trees on the east and west sides of the court you will end up with large invasive shadows over the service box. This will make play difficult because you can't tell where the baseline and sidelines are. Shade is certainly an important part of tennis, considering you need somewhere to sit out of the sun on a hot summer day. Supplying your tennis court with shaded tennis benches and not placing any tennis court equipment next to tall trees will improve your experience significantly.
To recap, orienting your tennis court 22 degrees from true north will cause the sun to strike your tennis nets and not your players eyes. And, you don't want to build your court next to tall shady trees. Effectively, if your tennis court net is lined up with a tree, it could be a problem.