Where can I find information about past versions of iOS and code-signing windows? I have an iPad 2 that is currently running iOS 5.0.1. I'm generally happy with it but some applications require a more recent iOS version. So I started to look into upgrading it, but the only upgrade that it offers is to iOS 7.

From the look of it I don't like the new design of iOS 7 too much and also upgrading to a version this fresh doesn't appeal to me. So my question is: is there a way to upgrade to some version of iOS 5.x or iOS 6.x instead of upgrading to iOS 7?
Currently, no, your only option is to upgrade to iOS 7. This is because Apple is no longer signing iOS 6 and the firmware signing status for iPad 2 shows iOS 7 as the only signed version.

Note: Lookup the signing status (or get the direct download links) for all iOS versions here.