Your final quest lies inthe Northern crater, but before you go there, there are some things you can still do.
First, there are some new things in Disc 3. Enter to Cosmo Canyon with Red XIII in your party for the last big event with Bugenhagen. Bugenhagen will speakc with red XIII for a moment, and then give him his best weapon, the Limited Moon. In the Bone Village, a lot of stuff that you might have not have gotten earlier and is now unattainable can be excavated, like the Huge Materias and W-Item.
Next, go to the Downed Shinra Plane, which can be found as soon as you get the submarine. It's underwater, around a corner in the area near the Key of the Ancients. On the map, its location is inside the little bay near Costa Del Sol. In your wanderings, you should find it eventually. (Btw, if you can't find it, just follow UW Weapon around for a while. He'll eventually lead you to it.) Ribbons are almost a nessecity in this place, so be prepared. The enemies here are very dangerous, much more dangerous than the two Turks you come across in the next room. All the hassle, however, will pay off when you locate all the items hidden around here: Heaven's Cloud (one of Cloud's best weapons), Escort Guard (works like a Minerva Band, but for a man instead), 2 Megalixers, Spirit Lance (a weapon for Cid), Hades Summon, Highwind (Cid's level 4 limit break), Outsider (a new weapon for Vincent), Conformer (Yuffie's ultimate), and the Double Cut materia, hidden in the upper righthand corner of the lab. (The room with the Mako Reactor.)
The other place of interest underwater is near the tunnel leading to the Key to the Ancients, and is also reachable after you get the sub. Just go to that deadend where the Key was, then turn around and head out and right. You should find somewhere along the line a little opening, which leads to a tunnel, and eventually, a circular chamber. Surface and you'll be directly in front of a waterfall. You can get out of the sub by the little beach area there. Put Vincent in your party and head into the chamber behind the waterfall, where you'll find a mysterious woman from long ago. Finally, the mystery of Vincent's mysterious past is revealed! If you come back here a little later, have Cloud look at the alter at the top of the room. You will find Vincent's Level 4 limit break and the Death Penalty,his best weapon here. The Death Penalty does damage based on how many enemies Vicent has killed.
Well, do you have everything you want? Are you set to go? Then go back up to the crater and enter the Final Dungeon!
If you think you've done everything else that you want to, then feel fre to enter the Northern Crater. To enter, just fly the Highwind over it and land it. You can actually leave here once you've entered, so don't feel like you're stuck once you've entered. The route is fairly straightforward, so grab the Save Crystal (to be used later), and the various source items laying around. The Dark Dragons here know Dragon Force, an enemy skill you'll have to manipulate them for. I've also found that they are some of the best enemies to fight to get your second Limit Break in any level. First, equip who ever you want to learn the next Limit Break with a mastered "Cover" materia, then find a Dark Dragon. Have somone cast Regen, have another person constantly use Magic Hammer (so that the Dragon doesn't cast Ultima on you), and just let the person get their Limit. I used this to get all of Cid's second Limit Breaks. (Btw, if you use this trick, then head back to the Mythril Cave after you get every one's second limits. You can have basically everyone learn all their Limits fairly quick.) Also, the Parasites know both Magic Breath and Level 5 Death, both of which you'll also have to manipulate them for. Watch out when you're getting Level 5 Death--make sure you're not all levels that are multiples of 5, or you'll end up killing your whole party.
In the second screen, there is a hidden HP Absorb. Just head left from the starting point, and climb up to the top left ledge. From there, go right behind the rocks and grab the semi-hidden materia. If you look really carefully, you can see it. Now, to get to the next screen, stay right as you go down. The next screen seems a little complicated, but a little experimentation will get you where you need to go. Try going directly right of the first door, jump down, go in the door, go around, and jump down some more. The chests aren't really worth it--all they contain are sources, a megalixer, and some Hero Medecine.
Now, when you arrive at the bottom where your party is, you'll have the option of splitting them up to get them to find stuff. Unfortunately, they're not very good treasure hunters, and while you can send them to find stuff, you're better off taking both routes to make sure you got everything. Now, if you want to do some AP-raising so that you can go back and tackle the optional Weapon bosses, go left. Tell everybody to go left as well. Then, at the next fork, you and your two party members go up, while everyone else goes down. In the Left/Up area (it looks like the inside of somone's ear), you can find the following: Magic Source, Hero Medicine, Shield materia (offers great protection, but only to one person), Imperial Guard (can also be gotten in the Huge Materia Mission at Fort Condor), Vaccine, W-Magic, and Command Counter. As far as AP-raising, there are the Magic Pots, who will be invulnerable until you give them an Elixer, and who are worth 1000 AP and 3000 EXP each. Also, there's the Movers, who attack in packs of threes, giving you a grand total of 2400 AP when you win. With some double-AP weapons and armor on, you can get a great many materia mastered in no time. You will also come across Master Tonberi in this section, a cloaked lizard with a star on his head that is much faster and stronger than his cousin in the Battle Square. There's a trick to killing him, though. When you first get the chance, have somone use Hades on him. Now, he's Stopped and Poisoned. Have Yuffie equiped with the Conformer and a Morph materia, and you can easily Morph him. You'll receive a Ribbon for it. Finally, in the last section of the Left/Up route, the W-Magic materia is hidden in the trees, and the Command Counter is hidden in the white glowing thing at the bottom. Be sure to look carefully for them, becuase they are impossible to see.
Talk to your people and see what they've turned up. They should have gotten just about everything from the Left/Down route, but since you're going back that way anyways (to get back to the top to either leave the cave or use the right route), you should double check as you go up. If they missed the Mega-all materia, you'll need to get it yourself, which can be tough. In the first screen, directly up from the entrance, is a little pedestal in front of a waterfall with the Mega-all bouncing on top of it. To get it, jump up onto the pedestal, and press O as quickly as you can so that Cloud will pick it up during his split second on the pedestal. If you missed it, jump back and continue with the O button. A turbo controller helps. Now just follow the path up, checking to make sure there are no unopened treasure chests.
Well, whether you do it now or wait until later, you'll want to do the Right Path eventually, so here it is. First of all, the reason we're going down both paths is to first, get all the treasure, and second, get all the enemy skills. Why? Because there's some pretty good ones down here, that's why! The right route not only contains a second Mystile, a Tetra Elemental, and some other stuff, but it also contains Angel's Whisper (held by Polensalita, who must be manipulated to get it), Shadow Flare, and Pandora's Box (both of which are held by the Dragon Zombie), and Death Roulette (held by the Death Dealers). Do yourself a favor and be careful when trying to get Death Roulette. To be safe, cast Death Force on your people, to protect them from Roulette. Angel's Whisper is worth it's weight in gold, for it completely heals anyone, even dead characters. What's more, it only costs 50 MP. Shadow Flare and Pandora's Box are very powerful attack spells.
Well, that pretty much does it. When you're done everything you want to down here and up above in the rest of the world, you have no choice but to find Sephiroth and deal with him.