Located within a small pond nesled in between the mountains is a waterfall. Behind this waterfall is Lucrecia's cave. Accessible through a Golden Chocobo, Black Chocobo(I guess), and the submarine. Go in there and find out about Vincent's past. Go in there again to get Vincent his Ultimate Weapon and Limit Break.
In the top northeast corner of the map there is a small island. The map does not show this island but it is there. In it are the Knights of the Round Materia. It can only be reached by access of a Golden Chocobo
if one of your character is hit and his hit points go to 7777 he will hit all lucky 7's. The character will enter berserker and attack non-stop doing 7777 points of damage each time. The enemy won't even have time to retaliate. But when the battle is over, he will go to 1 hit point.
Get over 100 wins by fighting battles. To see how many wins you have, get in the Highwind or ride a Green, Blue, Black, or Gold Chocobo ever so slightly south and a little ways to the east of Midgar City, where you'll find a cave surrounded by mountains with a river nearby. Inside the cave is a sleeping fellow who (usually) tells you how many wins you've gotten so far. Not only do you need to have over 100 wins, but the last two digits have to be the same (100, 111, 255, 733, etc.) When you have the correct number of victories, talk to the sleeping man. He'll toss and turn, then give you an item (Mythril). Next, go to the house on the penninsula near the Gold Saucer (you should recognize it since it's full of weapons inside). Talk to the man in the house, and when he gives you a choice, pick the top option. You'll lose the Mythril, but you now have the choice of opening the long wooden chest by the bed to get a Gold Armlet, or examining the metal lid on the upper floor at the end of the walkway to get the manual for Aeris's Level 4 Limit Break.
Head due south from Cosmo Canyon in the Highwind, then go a little to the west. You'll see an island that's part dirt, part grass, with a smaller grassy island nearby. This isle doesn't appear on the Map, but if you land the Highwind on the grassy plain and run around in the dirt long enough, you can fight Sabotenders (better known as Cactrots; those little cactus guys from FF3)! You can't get Rename Cards from them or anything like that, but it's kinda fun fighting them. Actually, the name of this island is 'Cactus Island' so it makes sense to find them here. To get to the second isle, head for the two islands near to each other on the northeastern edge of the map. Then go north (and a little more to the east), and you'll come across an oval-shaped island surrounded by mountains. There's a cave entrance here, but you can't land there in the Highwind. For more about the island, refer to the Bonus Areas part in section 6. The name of this place is 'Round Island'.