Starting with Warcraft III patch 1.28, the game's data is stored at C:/users/<your username>/Documents/Warcraft III and C:/users/<your username>/Saved Games/Warcraft III. If you have an existing installation, you'll need to migrate your Warcraft III data to these folders.
Note: New installations of Warcraft III will install the game's data to the new directory automatically.
The first time you run the game after patch 1.28, it will ask to run the game as an administrator to move your current data to these locations. Click Yes to start the game when prompted and begin the migration process. Once the migration is complete, you can run the game normally without it requiring administrator access.