I may need to setup a RODC - Read Only Domain Controller - at various branch offices and would like to know if I can do this with a Core installation of Windows 2008 Server? If so, are there any reasons for or against doing it this way?

You certainly can configure a RODC on a core installation. Will the server be used for anything else? If not then you won't really need a GUI, you can just use management tools to manage it remotely. As long as you feel you are able to do so

You can also run a Read Only DNS server on there

So I assume once it's setup it won't really require much maintenance, as I will make changes on a RWDC elsewhere and they will just cascade down?

Yes, that's exactly it. Nobody can make any changes locally so it's less likely to require any maintenance.

You can also run a Read Only DNS server on there

Hi,
Installing a Read-Only Domain Controller (RODC) is not much different than installing a domain controller normally.
The RODC is designed primarily to provide additional security in a database to an Active Directory server is not physically secure. Installing an RODC in a base install of Windows 2008 does not provide additional security.
Thanks.