Toy Box (Galaxy Toys)
The Toy Box is a good place to earn experience fast near the beginning of the story. Many enemies appear in this world, particularly in Galaxy Toys. You can also easily take out waves of Heartless by piloting the Gigas exclusive to the world.
The Caribbean (Sea Battle)
For mid game, it is recommended to take on the fleet of Heartless aboard your ship in The Caribbean. Defeating enemy ships nets you 300 to 400 experience points. The Heartless ships can easily be dealt with by attacking the glowing spheres on the hulls of the vessels.
Keyblade Graveyard (Battlegate No. 0)
The Keyblade Graveyard is the best place to level-up towards the late stages of the story. Head to the labyrinth and access Battlegate no. 0. This pits you against waves of fairly strong Heartless, allowing you to farm around 11,000 experience points in a single run.
It is recommended to gain a few levels here before taking on the final battle at the Keyblade Graveyard.
Clearing Battlegates is the most efficient method of gaining experience after clearing the main story. You can easily raise your level to maximum (Lv.99) by running Battlegates multiple times.
Olympus Battlegate no. 1 (Realm of the Gods)
Head to Mount Olympus Summit and climb the stairs to the Realm of the Gods. Battlegate no. 1 is directly ahead in the lobby. Enemies here can easily be defeated with Thundaga. You can gain a total of about 30,000 experience points in a single run, making it an ideal location to level up.
San Fransokyo Battlegate no. 12 (Northern District of the City)
Fast travel to the Northern District of the city in San Fransokyo. From your starting location, get on the roof of the building on the southwest to find the Battlegate.
Battlegate no. 12 allows you to farm experience quickly and is even a good location to obtain rare synthesis materials, particularly Wellspring Crystals.