I'm almost certain it would have been Quayle. Even though he was not very well liked, there was enough of a base to vote for him. He also would have had much more recognition than even Dole. Plus, he probably would have had the endorsement of a sitting two term president.
And of course you have George W. and Jeb who by 96 had their own political careers and probably would have had their names tossed up.
George Jr. was elected as the governor of Texas in 1996 and Jeb won the same in Florida in the same year, or so I've read, so their political careers would probably not be established at that time, although(little known fact) "Dubya" ran his father's campaign in 1988.
Not trying to hi-jack a thread or anything and I'll start a new one if it gets too out of hand, but I think a more interesting question would be who would the republicans have run in 04' if Gore won in 2000?