Is my vote for President and Vice President meaningful in the Electoral College system?

Yes, within your State your vote has a great deal of significance. Under the Electoral College system, we do not elect the President and Vice President through a direct nation-wide vote. The Presidential election is decided by the combined results of 51 State elections (in this context, the term "State" includes DC). It is possible that an elector could ignore the results of the popular vote, but that occurs very rarely. Your vote helps decide which candidate receives your State's electoral votes.

The founders of the nation devised the Electoral College system as part of their plan to share power between the States and the national government. Under the Federal system adopted in the U.S. Constitution, the nation-wide popular vote has no legal significance. As a result, it is possible that the electoral votes awarded on the basis of State elections could produce a different result than the nation-wide popular vote. Nevertheless, the individual citizen's vote is important to the outcome of each State election.
NARA | Federal Register | U. S. Electoral College