The two most obvious choices for this answer would be Ronald Reagan and Bill Clinton. Both were two term Presidents who had many accomplishments. However, many of Clinton's accomplishments were the result of his failures: the balanced budget was the result of him failing to reform health care, and Congress's Contract with America. Reagan certainly inspired the nation, but he left office with triple the debt he began with, and his deregulations had substantial unintended consequences, such as arbitraging and the S&L debacle.
The best President since the 60s was sandwiched between these two: George H.W. Bush. He put his career by the wayside to fix several of the problems created by the Reagan years. He bit the bullet on the S&L bail out, and raised taxes sufficiently to eventually reduce the deficit, which benefitted Clinton.
In addition to putting a second term in jeopardy, he created one of the most remarkable alliances in the history of this country when he got Arab nations to agree to allow us to use bases and air spaces to drive Iraq out of Kuwait. His agreement with them was that we would leave as soon as the job was done, and we would not send hit men in after Saddam Hussein (although they agreed he could be killed if it were done in the course of the barrage). He honored his agreement after about a week, and would be criticized by throngs of people who would put honor behind assassination.
If the election would have been immediately after Desert Storm, no one could have beat him. However, a couple of years passed, and people pointed at what seemed to be a rather stagnant economy. Bill Clinton used it against him with his famous quote "It's the economy, stupid." GHWB contended that the economy was beginning to recover fully, which proved to be true as soon as the fourth quarter 1992 data were released.
GHWB is often forgotten in these types of discussions, but his administration solidified the legacies of both his predecessor and successor, who are the two most obvious choices by those who only want to declare the two-term President from their party of choice was the best.