Is there a way to add a column to the "orders" page under the sales tab? We would like to be able to filter the customer orders by their location (state). Thank you!
Yes this is possible, but you have to build a custom module which will extend the magento default functionality for that issue.
Yes, sure. You can add more or custom order grid by add on plugin or magento extension. Maybe consider about some good provider: Magecheckout, AheadWork, Amasty...
Without custmisation or additional extensions default Magento can't do this - Luckily I would say the best extension to allow you to do this is FREE - https://www.magentocommerce.com/magento-connect/enhanced-admin-grids-editor.html it will do what you want nicely and also allow you to customise all the other grids (or or can just leave them as is if you prefer.)
Once installed to get the state column you will need go to the orders grid select Grid Customization > More options > Custom columns > select state and hit apply.
You will then have a state column as below - sadly (for me atleast) this is option and sometimes a text so it's not a dropdown filter but rather a text filter but it does still work.