I'm trying to reconcile my accounts, and am missing transactions from my suntrust account from 06/01 to 06/25. Is there a way to get these through the "banking" tab?

Initial bank connections will at best give you 90 days prior. There is no way to go back from within QB and grab missing ones or ones prior to the 90 day cutoff.

You can, however, navigate to and log in to your bank website and download transaction history and then import same in csv format

That won't happen because suntrust doesn't allow for downloading of transactions unless you want to pay $25/month