The electoral college is a necessary part of the compromise that allowed our constitution to pass. It balances the power of the large and small states.
The electoral college ensures that each state has the same say in electing the president as it does in passing laws in congress.
The only logical change to the law would be to apportion electoral votes by congressional district. A presidential candidate would receive an electoral vote for each district he won and the statewide winner would receive two electoral votes representing the state’s senators.
This would ensure that conservative areas in states like New York and California would have their votes count, while liberal areas like Austin, TX would have their votes count.
A national popular vote could make the big city vote fraud a major factor in the presidential race.
Even that change would require a constitutional amendment. Article II, Section 1 specifies that the method for appointment of electors is to be determined by each state's legislature.
States are already free to do what you propose. I believe that there are two that do. The states can't, though, be forced to do so without an amendment.