EDIT: People are the bigger disccusion thread (https://news.ycombinator.com/item?id=6502756) are saying that it's possible to update without deleting/restore by downloading the ipsw and alt+click the "check for updates button".

--- Original: --- Booting to recovery mode (http://support.apple.com/kb/HT1808) and clicking restore will download the 7.0.2 firmware (no need to alt+restore), wipe the phone, and update to 7.0.2

I was getting offered 6.1.3 and not 7.0.2 because my itunes wasn't updated to 11.1+.

Before booting to recovery mode, copy over your camera roll with image capture/aperture/iphoto just in case your latest backup (iCloud or iTunes) isn't up to date.

Same issues... just download the iOS 7.0.2 image from my developer account and updated the phone.

Was quite quick and no settings changes or loss.