I just got a Nexus 7, and it’s my first Android device since Gingerbread. I’ll write more impressions later, but I wanted to post a quick note for someone else Googling this like I was, which didn’t turn up an obvious answer to the question: “Where do downloads go on the Nexus 7?” Note that this answer is probably relevant to any device running Jelly Bean, perhaps earlier.
Answer: On the “All Apps” screen (tap the circle icon with 6 squares in it on the main screen), theres a “Downloads” app that shows downloaded files from Android’s version of Chrome.