Anyplace in L.A. to get unsweetened bubble tea?
That might be a tough order, because most all places cook the boba (tapioca) balls in a thin sugar syrup before they're cooled and added to a boba drink.
I suppose you can order a plain nonsweetened black or green tea without the boba, but then, that's just tea. And you can get that anywhere.
I apologize for complicating your question, rather than answering. I suck, I know.
I think your best bet would be to find vacuum packed boba at a Chinese market and cook it at home. There are some that are par-boiled, vacuum seal, and all you need to do is boil for 5 minutes. They will look dark and black, unlike the completely dry ones that look a little powdery and more brown.
Professor Salt is absolutely correct that a lot of places cook the boba in a sugar water, so it will always be sweet.
Green Tea Terrace will make things to order-- you have a choice of (actual) milks, sweeteners (sugar or honey, and I don't think they have agave, but the now-closed T on Fairfax did...), unsweetened-ness, etc.
That said, the boba you'll be getting was immersed in a syrup before it was dumped into your cup of unsweetened milk tea, so it'll get sweeter.