I recently downloaded the Armory Wallet for my Mac. It appears to work great, but is there any way I can purchase Bitcoins via an exchange on the wallet interface itself? If not, what should I do?
No, in general wallets are just tools to manage bitcoins already in your possession. The only exception I can think of is Mycelium, which includes a functionality to find buyers and sellers nearby.
To find out how to get bitcoins, check out How do you obtain bitcoins?.