Finding a good Martial Arts school is definitely tricky business. Due to a number of factors but the biggest one being, you don't know (assuming you ever find out) if your being trained by someone who is qualified or not just trying to swindle you, until you've been training under them for a number of years and find yourself in a situation where you have to use it against a trained opponent either on the street (if you were attacked or something) or in a match against someone from a different school (or a trained boxer for that matter). Obviously this gives 'learning the hard way' a very dangerous spin.
However finding a decent school isn't impossible although, you might end up in a situation where you can only learn the forms and techniques from someone but have to find someone else to teach you their purpose and application. Tai Chi is a perfect example of this, as you generally find someone that can teach you the basic forms without much difficulty, but finding someone who has a clue as to how use the style in a combat situation is very rare. They either have no concept of Tai Chi as an actual 'martial art' or when faced with a simple jab, their technique... flat out sucks for lack of a better term.
So here is my advice:
for a Japanese martial art, I would try to find a Judo, Jujutsu, Karate, Kenjutsu, or something similiar (I'm very 'iffy' about Ninjutsu to be frank; as everything I've read and seen of it makes me think that someone a few centuries ago just stole some techniques and forms from Samurai [who sometimes would get training in Espionage or stealth, depending on the school], then proceeded to make everything very esoteric sounding to play on the common folks fears) in a school that has a direct lineage leading back to Japan or is affiliated with a traditional ryu. As this means you can be more confident in the level of training you will receive and reputable Japanese martial arts schools might be able to direct you to someplace where you can further your training.
Chinese martial arts on the other hand.... it's a nightmare ( in an earlier post I mentioned a documentary called 'Needle through Brick', you can find it online and even watch it for free still I think, but it provides a good summary of the situation of tradition Kung-Fu), because between the Japanese occupation, and the Cultural Revolution, Kung-Fu was almost wiped out. This means that their are very few individuals, even in mainland China, that are qualified practitioners or that teach an actual system of martial arts that isn't simply a syllabus of forms approved by a group of officials that is made up of kung-fu stances, done in a way that are no longer useful for combat, and then a bunch of very flowery acrobatic movements that are useless as a martial art. Their are some legitimate schools out their, although the best teacher you could find would probably be some person, who literally just operates out of their garage, backyard, or a park. For the softer or internal styles ( e.g. Tai chi, Bagua-zhang, xingyi-quan) you might be able to find at least a school that will teach you the orthodox forms, although you likely have to continue training elsewhere, but at least you will know the basic forms which is a big step.
I know I sound super negative, just don't want you (or anyone else here) to be one of the many who devotes years of their lives and enormous sums of money to learn from a hack. If you want some help or are looking at something in particular, I can do my best to help (although I am by no means an expert, but I'm better at spotting something fishy than many I suspect), so feel free to send me a PM if you'd like.