We have a secure proxy setup - meaning we don't allow access to the web except for defined destinations. What are the destinations I need to allow through our proxy to enable to BOINC to send traffic on port 80 and 443?

You'll need to OK the url for each project that you want to run.
Some are here. Note the line just above the list, which has a link to a larger list.

I'm not sure if it concerns you, but at least for SETI, some servers (upload/download/scheduler?) are reached on an address other than the project's (setiathome.berkeley.edu), namely on setiboincdata.ssl.berkeley.edu

Gruß,
Gundolf

---

Computer sind nicht alles im Leben. (Kleiner Scherz)

It's likely that most of the 100 plus projects have multipe urls for their servers.
Hiowever, once you let BOINC attach to a project, you'll soon find out which url's are failing on downloads & uploads, and can let those through the proxy as well.
And you can also ask on the web sites of individual projects for a list of urls.