Adlai Stevenson (he's pretty much the last governor of Illinois who didn't go to jail) and Al Gore would be my picks.
Stevenson was very, very smart, and would probably have dealt with the leadup to Vietnam War better than Eisenhower or Kennedy (remember he ran in 1960 as well). He might have begun some version of LBJ's Great Society programs earlier as well.
Yeah but did he have the political support and power that LBJ did to take on intractable issues like civil rights? LBJ's arm-twisting and insanely strong political savvy was nearly without equal in his time. It was what basically let him keep what was left of FDR's New Deal coalition together before he finished it permanently with civil rights.
Also Vietnam turned into a huge fuck-up because of the exodus of advisors brought on by McCarthy and his anti-communist hysteria. A president Stevenson probably wouldn't have been able to significantly curb McCarthy any more than Eisenhower, who both opposed McCarthy and shared a party. McCarthy would have turned it into a partisan squabble if Stevenson tried to challenge him. We'd still our advisors and we'd still probably have a costly boondoggle abroad. The best hope for a more successful Vietnam is to support Ho Chih Minh early on when he was fighting the French occupation and before he turned to the Soviets and communist ideology in general for assistance, Stevenson might not have politically been able to stir the pot and do that, not with Hooveresque types who started to see communists behind every anti-colonial movement everywhere.
Edit: I'd have liked to have seen a President Al Gore... or Howard Dean, perhaps none of that stupid "I have a scream" fuss.
A Few I'd Liked To Have Seen...
Samuel Tilden instead of worthless Hayes
Al Smith
Bobby Kennedy
(Mildly ASB given the time but...) Frances Perkins or another New Dealer.
Although theoretically I would be happy with a garden shovel replacing President Andrew Johnson I would have to venture to guess that William Seward is a favorite of mine, Ice Box for President!