Got a minute, Leonora?
The phone book lists most schools. The adult education programs feature others. Colleges and YMCAs might also have martial arts clubs, too--check those out.
Finding a local tournament from the outside is sometimes difficult. Tournament marketing is directed 100% toward existing students. If you do find one, though, check it out. Look at patches, talk to students, talk to judges, etc.
As far as finding the garage-dojos that can be some of the best (or worst), you're out of luck being a stranger.
Once you have a nice big list of possibles, check them out. Ignore certifications and trophies. They're so common as to be meaningless.
Look for higher-rank students (brown & black belts in karate). If the class is all lower belts, it's either new or the students are dropping out before they advance.
Watch how the instructor treats the students. Does he lose his temper? Does he play favorites? Is he insulting? Don't sign up there! Look for someone who's fair, supportive, and encourages learning.
Watch how the students treat each other. Are senior students elitist toward their juniors? Do they work together? Are beginner separated from experienced students, even for a while (that's good, because they can benefit from some close attention before joining the rest of the class)?
Watch the activities. Is there sparring? If so, is there contact? Is that what you want? Do the students work primarily on their own, or with a partner? Does the class take safety precautions? Do students pay attention?
I would not recommend ju jutsu unless you are very flexible and have good insurance. Grappling styles, like ju jutsu and judo, have more serious and more frequent injuries than striking arts like karate or tae kwon do and most kung fu styles. Grappling injuries especially include joints, like the wrists, knees, and ankles--injuries that are long-lasting, life-affecting, and slower to heal.
Sorry for the long post, but you asked the $64,000 question. <img src="/images/graemlins/smile.gif" alt="" />