The definitive moderate Republican may have been Dwight Eisenhower, and I have heard plenty of Democrats praise the Eisenhower Presidency. He went along with Supreme Court rulings that outlawed segregationist practices, stayed clear of the McCarthy bandwagon, and let McCarthy implode.
gray -- did not vote in 1952 or 1956
white -- Eisenhower twice, Obama twice
deep blue -- Republican all four elections
light blue -- Republican all but 2008 (I assume that greater Omaha went for Ike twice)
light green -- Eisenhower once, Stevenson once, Obama never
dark green -- Stevenson twice, Obama never
pink -- Stevenson twice, Obama once
Two Presidents who had very different backgrounds -- but similar temperaments.