Where to put the adjective when asking for something that comes in multiple sizes?
I'm not a linguist, just a native speaker. My opinion is that 大 should go before 杯, i.e. 我要一大杯咖啡, since I have never heard anyone said 我要一杯大咖啡.

Words like 杯 are called 量词(sorry I don't know the exact term), and the adjectives about amount are always placed before 量词. For example, 
一大碗饭= a bowl of a lot of rice， 一大把花= a bunch of many flowers.

Maybe this solution is not satisfying; sorry I can't explain it in detail. 量词 is actually quite sophisticated, and is often omitted when translated into English. I hope this article will help (well it's written in Chinese).