For the benefit of others here is what I have done to fix my issue. You do not have to DFU or Reset Content Settings as suggested by others online.
Hopefully an official fix will be published soon, until then feel free to try the below steps. My issue occured on a 4s 5.1.1 upgrade to iOS 7, but others may have the same or similar issue.
After upgrading to iOS7 on a 4S, I was unable to access iTunes or App Store.
You will receive an error a message saying that iTunes or App Store is unavailable when opening iTunes or App Store.
Content for iTunes and App Store is blank even though you have connectivity.
Close iTunes and App Store, Select Settings -> Safari -> Disable 'Do not track' and set 'Block Cookies' to never.
Now back into Settings -> iTunes and App Store and make sure you have signed in with your Apple ID and Password.
Then re-open iTunes or App Store and they should be now working as normal.
If you want 'Do not Track' enabled you will need to test if this breaks your App Store or iTunes access as it seems to revolve around cookies being blocked by third parties which in this case is Apple iTunes or AppStore Service.