In OTL 2004, John Edwards was viewed as politically inexperienced and ready to walk into the Oval Office should Kerry be unable to carry out his duties as president. Who would have been a better running mate for John Kerry? I know Kerry really had no chance in 2004 given his history and the illusion of victory in Iraq but, I'm asking out of curiosity.
No chance? The election was exceptionally close; Kerry certainly had a chance if things had gone a bit differently (although I suspect that 04 was a poisoned chalice for anyone who did win). And, honestly, in '04 I don't think Edwards was a poor choice; he brought youth and energy to the ticket, while Kerry had the experience. This was well before the sex scandal that sank his career, and we can't let that color our views of how he was seen at the time.
As for who would be better? You would want someone who could appeal to the base and thereby further to the left than Kerry, and someone younger and a bit more charismatic. Also, you are going to want someone not from the Northeast, to help balance the ticket. I would almost say someone like Feingold would be an interesting choice (very popular with the Progressive base, his singular vote against the Patriot Act would juxtapose him against Cheney well), but I doubt he would want to give up his Senate seat. Also, I'm hardly unbiased.
So, lets look at the criteria:
1) Younger than Kerry or who can at least give off the impression of youth and vigor
2) Popular with the base of the party and probably to Kerry's left.
3) Preferably someone from the South, Rust Belt, Upper Midwest or Great Plains (I would veer away from the West Coast, since those states are solidly Democratic at not swing states. 2004, like 2000 was going to hinge on a small number of states)
Interesting thought: Harold Ford Jr. He was secure in his Congressional district in Tennessee, was viewed as a major up-and-comer in the party at the time, and definitely had ambitions for higher office. In OTL he ran for Senate in 2006 and lost narrowly. Also, being from a perceived swing state and being African-American wouldn't hurt, either.