Adding new SharePoint web applications on port 80 is easy by associating a host header name, but I was unable to view the site collection in the new web application with IE - the login dialog box would show three times, and then just a blank page, even though my account was the primary site collection administrator.
Turns out that in Windows 2008 R2 it is necessary to disable the loopback check. Open the Powershell ISE or console (as administrator to get sufficient registry permissions!) and run the following script:
New-ItemProperty HKLM:\System\CurrentControlSet\Control\Lsa -Name "DisableLoopbackCheck" -value "1" -PropertyType dword
Thanks to Ignacio Montenegro of IGA Systems for that tip.