I don't like riding near cars or on busy roads.

Neither do we. Generally, we try to keep our routes on quieter roads with ample shoulders for safety. Some rides are chosen for other reasons, like scenery, but if you ask anyone in the club, they'll tell you where their favorite ride locations are. It takes some time to get used to riding with traffic, we've all been there. The best way is to ride with people you're comfortable with and take your time.