Are you looking for JSA exclusively? Authentic kenjutsu can be difficult to find, and may entail some travel (sometimes to Japan), but sometimes that's what you've got to do. I travel over three hours to train with my Provost. For western sword arts, there seems to be an ARMA chapter in Austin, if that interests you. Likely they're focused on longsword or rapier, and a fair amount of grappling. As a general rule, instruction at an ARMA chapter is likely to be very good.
There's a good JSA subforum on swordforum.com that could be of some assistance as well. Remember that there are many folks out there masquerading as "authentic bujutsu" which are anything but. Do your research. If you're looking for koryu stuff EXCLUSIVELY, then you should check out koryu.com for an exhaustive listing of authentic classical Japanese arts.
Best regards,
-Mark