Nixon continues on as a personally polarizing but very supported president. He works to craft a legacy and create a Churchill inspired Conservative party out of the Republican party, uniting various interests under the umbrella of Conservatism and the GOP. Not really all that different of a situation, given said plan really mirrors what exactly happened. Possibly it would have been more successful and more hastened, since it would take till about Michael Dukakis in 1988 for Liberal to become really a 4 letter word and for Liberalism to be decimated as a political force for generations. Nixon's legacy is carefully shaped in the exact manner the Nixon Foundation still does, and all the same there will be many people who shoot holes in the glorifying of Nixon and take major criticisms of him based on the way he already was and what was already known pre-Watergate. It's just that there won't be a Watergate to
totally demonize him over.
Also, don't expect some great Liberal administration. Nixon wasn't "the last Liberal president" as he is often called. Many of those things he is lauded for and which are claimed as Liberal were the result of a lot of good government Republicans, and Nixon is recorded as bemoaning them and being embarrassed by them, and wanting to get rid of many of them, meaning he could potentially have repealed them given an unhindered administration. I'll point you to the Timothy Naftali interview:
http://www.c-spanvideo.org/program/309875-1
http://www.c-spanvideo.org/program/309875-2
Also, Nixon hounded John Lennon up until the very end trying to get him kicked out of the country and wiretapping him and otherwise using government force to harass. I'd expect that to continue, possibly successfully.
Come 1976, there is no dirty Washington need for an outsider, so no Jimmy Carter. Nixon is also in a prime spot to nominate his favored successor. That could be John Connally, but I get the feeling that the Republicans would rebuke any attempt since Connally was a turncoat (Democrat who turned Republican) and he wasn't in any position to be president via offices held; it's just that Nixon liked him. No, Connally would not be vice president in lieu of Agnew in this universe. Firstly, Watergate was separate from Agnew's resignation. Secondly, Connally turned down the office when offered because he viewed it as worthless. You potentially have Reagan in 1976. At the same time, Nixon thought he was essentially a moron. Not sure about what would happen there. Nixon could be all for it, in spite of that, especially if the GOP pushes strongly for Reagan in a tide Nixon cannot stand against, or he could back Reagan because he doesn't assume he'll do too much damage and may even assume he could control the White House via the influence of his people already there who continue in a Reagan* administration, or he could try to fight it for someone he'd prefer.