Here's what I think
If he doesn't get assassinated, he runs for reelection in 1964 on a promise to enact the Civil Rights Acts and voting rights act. He also considers dropping Lyndon Johnson from the ticket, but keeps him due to his Southern connections via Texas. Kennedy also states that he will start trying to bring military advisors home from Vietnam, yet doesn't go as far as to say he will end involvement. He does however, as in OTL authorize Diem's assassination, and does keep a small amount of advisors there, but his plan is to leave Vietnam with a more popular regime, and pull out at some point in the future
Anyway like Johnson in our Timeline, he defeats Goldwater handily, with Goldwater only winning the states of Arizona, LA, MS, AL, GA, and SC as in OTL, plus Utah, Idaho, Nebraska, Florida, and virginia (states that gave less that 55% of their vote to Johnson) the margin of victory is close in a lot of states though. However, Kennedy doesn't need daddy's mob connections to win since he's fairly popular, and Goldwater is more abrasive .
Anyway, after JFK is reelected he passes the two civil rights bills, both of which pass, though many southerners are outraged, and some worry about the party either splitting, or the South going over to the REpublicans. Also, Kennedy places a new leader in South Vietnam and keeps advisors there, but brings enough home to satisfy. By 66 and into 67 Kennedy realizes the situation in Vietnam and calls all troops home. While Republicans see this as a defeat. Kennedy ensures that he wanted, peace with honor, and thus tries to have damage control.
Another problem Kennedy faces is riots in Northern Cities. While he does enact some of what in OTL is the Great Society, not as much is passed. Also, riots still occur in Watts and Detroit and other cities in 65 and 66. By 1967 things slow down. However things heat up with MLK's assassination which results in riots in many cities. Some blacks even blame Kennedy for not being as a big enough advocate for civil rights, but there is little he can do to help the situation other than offer his condolences to MLK. In the end he goes out of office with middling approval ratings. While many like that he didn't get involved in a foreign war, many also feel he became weaker on communism. His civil rights record is good for the time, but many today would say he could have done more. Where he does get extremely high marks is in getting America to the moon. In a way it is his victory against the Soviets.
In the end I think historians would probably think he was a better than average president. Not Up there with a Lincoln or Washington, or even an OTL Reagan, but he is remembered fondly by most, though conservatives think he lost Vietnam. I think by now though he'd be seen as better than average