Here is my canned response (I swear I should just copy & paste it to a document for easier reference...):
What is available within the distance you are willing to travel for consistent training? Narrow your search down based on that - it would be pointless to make a suggestion that seems perfect for you only to have the nearest teacher 200 miles away. Visit these locations and pay attention more to how they train rather than in what they train. Beyond that, talk to the teacher but also talk to other students and get their thoughts on classes there, just to get a feel for the school. If they are stand-offish or seemingly just want another punching bag, steer clear. If the instructor can't give concise answers as to the background of his/her method, steer clear. If they require you to sign up for any long-term contracts/commitments, steer clear. If they don't spar or otherwise practice with any real-world viability, steer clear.
I hope this helps.
If you have any questions beyond that pertaining to specific methods and/or schools once you have gone out and researched, by all means, ask again, as there are many knowledgeable individuals here in addition to the trolls.
EDIT based on updates: I've never heard of Sun Moo Kum Do nor Sun Do Sul, but I would guess them to be based on Korean martial arts, and upon a little research, that does seem to be the case. It looks like they blend aspects of Tae Kwon Do/ Tang Soo Do and Hwarang Do with sword patterns/sets added - no mention of bo ("bo staff" is redundant). Traditional Tae Kwon Do has no weapons at all in its purest form, and BJJ, while based on Japanese methods and altered to the point of becoming a system in its own right, does not train with use of the bo or any weapon to the best of knowledge and experience either. If you want to train in weapons, the choice is fairly evident, but follow my previously-mentioned advice to ensure it seems to be a good fit.
As an aside, and this is just conjecture, but the fact that Sun Do Sul is so obscure may be a red flag as well. Please be sure to do your due diligence to ensure it's a reputable martial art.