I live in So Cal, not sure why you are having trouble finding a Star Smog testing place, thats weird. Yes I know that's not the answer you're looking for. Where is So cal are you, depending where you live, I might be able to help you. Good Luck.
Look for any place that says Star test only or Star test and repair. These are places that have higher levels of scrutiny by the state (monthly checks) and are assigned to vehicles with histories of cheating and gross polluters (the supra falls into this category sadly).
This site has a search tool that can help you find coupons and locations for star test centers by zip. It is not perfect, the place I go to is not listed for example when I put in my zip, but it will point you in the right direction.
What is the difference with a regular smog station and a STAR smog station? You received your DMV renewal notice and discovered it says Smog Certification Required at a STAR Station. No need to panic. All this means is that the DMV has chosen your vehicle to be inspected at a STAR certified smog...