Well there are plenty of threads about this already, but I'll rehash the general consensus (or at least my thoughts) in an easy to use format:
1964 Election
-Democratic Nomination: Kennedy is challenged by George Wallace in the primaries. He is less successful than he was in OTL because of Kennedy's appeal among many of the same ethnic working class voters that supported Wallace. The President easily wins renomination. Kennedy keeps Johnson on the ticket. He had no personal problems with LBJ (though his brother did) and though he may have wanted a friend with North Carolina Terry Sanford on the ticket, it's unlikely he would have taken such a big risk.
-Republican Nomination: Goldwater defeats Rockefeller for many of the same reasons as OTL. Rockefeller's divorce and remarriage harmed him greatly among conservatives, and whoever the President was made little impact. Goldwater wins the nomination after winning California and chooses a moderate, such as Pennsylvania Governor William Scranton, as his running-mate (he only chose Bill Miller in OTL because he bugged Johnson).
-General Election: Kennedy and Goldwater campaign across the country. Kennedy's theme is peace and prosperity, while also addressing issues like Civil Rights and poverty. Goldwater attacks the President for being too soft on Communism (the withdrawal from Vietnam being the obvious example) and for presiding over the continued expansion of the federal government. They engage in a series of televised debates, in which Kennedy's style and Goldwater's "wonkish" delivery portray a stark contrast. The President easily wins reelection, but loses the Deep South and several Western states to Goldwater.
Foreign Policy
-Vietnam: Kennedy begins the planned withdrawal of military advisers in 1963 and 64. Military and economic aide are maintained. There is some debate as to whether Kennedy would backtrack and deploy ground forces if the Communists appeared likely to win.
-Cuba: An effort towards rapprochement is made by the United States. It's unlikely that there are any official policy changes, but the two nations will be on better terms.
-Latin America: Kennedy continues to push for greater diplomatic ties between the United States and our neighbors to the South. Trade and democratic reforms will be promoted. America may still intervene in the Dominican Republic revolution, but it is much less likely with Kennedy instead of Johnson in the White House.
-Europe: Stronger diplomacy between America and Europe, especially the UK. Kennedy was always interested in European affairs, far more so than LBJ. The United States maintains a better image there and our alliances are strengthened.
-China: Moving towards rapprochement but no "Kennedy in China" scenario.
-Soviet Union: Continued disarmament talks, possibly leading to an arms reduction agreement.
-Third World: A more active commitment to the Peace Corps and economic development of the Third World. Kennedy will maintain the goal of improving America's image in these nations in a way Johnson could not afford due to Vietnam. Particular assistance will be given to regimes combating Communist insurgencies.
Domestic Policy
-Civil Rights: Kennedy will not be able to get the Civil Rights Act passed in 1963 or 1964. The House Rules Committee will be forced to discharge the Civil Rights Act in early 1964, and the full House will pass the bill. But the Senate filibuster will remain intact until after the elections when the Republicans are willing to work with the President. It's likely this happens early sometime in 1965. Voting Rights may happen that year or a year later. It was more politically popular than the Civil Rights Act anyway.
-War on Poverty: Kennedy gets federal aide to public education passed in 1965. Minimum wage and Social Security increases will also be passed. Something like VISTA will also get passed, as may a Job Corps element.
-Medicare and Medicaid: These programs will have a tough time getting passed. Medicaid was much more politically popular among Southern Democrats, so that may get passed. Medicare stands a good chance, but still has to go through the conservative Senate Finance Committee. If this gets accomplished, it will be later in the President's term and after a long legislative battle.
-The Economy: Kennedy will probably get his tax-cut through Congress in 1964 or 1965. This would help stimulate demand, and the economy will continue to do well throughout the '60s. Inflation will be lower due to a smaller US commitment to Vietnam. This means stronger economic growth going forward as well.
-Urban Crime: The race riots of the 1960s will still occur, and may be larger due to the later passage of Civil Rights legislation. There was little any President could do to end the causes of the riots: poverty, lack of opportunity, and issues of a local nature.
-Counterculture: The counterculture will still arise, but will be smaller and less radical without the Vietnam War. The Beatles, Rolling Stones, and Bob Dylan will all be penning tunes that will resonate with a youth seeking a different life from their parents. If anything, the movement will be viewed more positively by the mainstream of American society because it won't be tied to draft card burning and an opposition of the President.
Legacy
-Kennedy's legacy would be generally positive. If he is able to get his domestic agenda passed in his second term, he will be viewed as a hero among Democrats and progressives. The New Frontier will be seen as a general success. But on issues of race relations and foreign policy, Kennedy will be criticized by conservatives. Urban crime and a "retreat" in the face of Communism will harm his legacy.
-1968 Election: The 1968 election would be much more favorable to the Democrats than it was in OTL. Johnson will probably win the nomination without too much opposition, as Bobby isn't ready yet and the party bosses want to put forward the strongest candidate. Johnson probably chooses Humphrey as his running-mate. However, the Democratic Party is still fracturing along class, gender, and racial lines. This began during the 1950s and will continue during this time. Civil Rights is a polarizing issue, and one which would define 1968. The Republicans will probably nominate Nixon, Romney, or Rockefeller. If they nominate Nixon, his moderate views on Civil Rights, but opposition to policies like busing and support for tough law and order, will probably give him a narrow victory.