Much of it depends on what qualities you are looking for in a President. My criteria comes down to who which President most closely adhered to the Constitution.
In general, the fist 15 Presidents (with a few exceptions) did a pretty good job of following the Constitution. Lincoln was number 16 and was probably the worst from the 19th century. Sadly, some of those first 15 are often at the bottom of the lists of "best" Presidents simply because they acted only within the outline of the Constitution.
Post Civil War, only a handful of Presidents have had the qualities I admire. The last good Democrat, at least in regard to the Constitution, was Grover Cleveland. He managed to tick off both parties by vetoing any bill that did not act within the confines of the Constitution. The only 20th century Presidents on my list would be Warren Harding and Calvin Coolidge.
In the past 80 years, we have not had a "good" President....at least not by my criteria. JFK and Regan were mediocre at best. FDR, both Bush, and Obama have all essential shredded the Constitution.