Little to no knowledge of Ninjitsu here, but plenty of knowledge in looking at MA schools. A couple points I think are important:
*See if you can get a schedule of classes (when they’re held). Stop by, unannounced, and watch a few classes (more than one.) One class, especially if it’s mostly black belts, will not give you the feel of the school. Any school that has a problem with a potential student dropping by unannounced is not someplace you will want to train.
*Talk to the head instructor. Also talk to students: about the instructors, about how classes are run, how often they train, how long it took them to get their current rank, how competitive the school is, how much fun vs. work it is, etc.
*Don’t sign a contract, at least not at first. Be very, very cautious around contracts. Many schools (a certain chain of karate dojos in the NJ/PA/NY area comes to mind) will give you a free intro lesson, and then try to corral you into signing a year (or more!) contract. Don’t. Give it a try first, at least a few months, before signing a contract like that.
*Regarding safety: Observe. Are the floors matted, sparring matches carefully supervised, plenty of space given when working out with weapons? Also - what’s the warm-up/cool-down like? Stretching out is one of the most important parts of a martial arts workout.
*Ask about cost, not just the basic tuition. Do you get a free uniform? High-end MA uniforms can be pricey. Need to buy your own weapons? Are there extra fees for belt testings? If you want to compete, you may need to join an official league or something (No clue if this applies to ninjitsu or not, I know TKD has 3 main leagues in the US).
*Nitpick with what Mtgman said about his wife’s school: length of black belt exam doesn’t matter. How intensely students are examined matters, and how much talent they can demonstrate. My black belt test took about an hour and an half. The only time I stopped moving during said 1.5 hours was to put on my sparring gear and then take it off - it was continuous. Don’t use that as a judge of the quality of a school.
Most importantly, have fun. If you don’t feel comfortable in the school, it’s not a good fit. You should naturally feel relaxed and interested.
Also - with regards to it being seedy - some of the best MA schools don’t have big flashy dojangs and whatnot. Example: one of the best TKD schools in the nation (well, best at producing tournament winners) started out in a garage in Texas. Appearances matter very little.