Now, the game has turned quite non-linear. You have access to nearly everywhere and can now go do anything still left or level up your party. You don't need to head down the Northern Crater right away. In fact, it could be dangerous if you do; some versions of the game may have a bug that prevents you from returning if you go down the crater. The Crater has a lot of really tough enemies as well, so it's better to stock up before going there.
You're left with a quite a few of things you can and should do. You can now collect various things that you can pick up at just about any time. You can also say goodbye to Bugenhagen and pick up Red XIII's ultimate weapon in Cosmo Canyon. Most importantly, you should level up. The higher level you are, the easier the big upcoming battles will be.
Secret Nibelheim cutscenes
Two questions still need an answer: How did Cloud survive the Nibelheim accident and join Avalanche? And how did Tifa leave Nibelheim and get to Midgar?
Two cutscenes become accessible only now, on Disc 3, in Nibelheim. Enter the Shinra mansion and go to the library. When you enter there, a cutscene occurs, showing how Cloud and Zack escaped fro Nibelheim. If you go to Tifa's house and play the special tune ("Do Re Mi Si La Do Re Mi Sol Fa Do Re Do"), you'll find a letter explaining how Tifa survived the same accident and ended up in Midgar.
The Northern Crater
You may want to equip someone with a Safety Bit to avoid the possibility of a level 4 death spell wiping out your entire party, or else make sure your party members' levels are staggered. Ribbons are useful for all the spells which cause sadness.
When you land in the crater, you find yourself sliding downhill. You'll end up in a chasm with spiral ledges going down. The cave leads back to the Highwind. The first chest contains a Save Crystal, which you can use that to deploy a save point anywhere in the Northern Crater. The other chest contains a Guard Source.
The next area has chests containing Power, Magic, Guard and Mind Sources. Press to climb the ledges where it's possible. Also note that at the topmost platform, half-hidden behind a stalagmite, you see something glittery. Climb to the top-left ledge and check it out - it's an HP Absorb materia.
Then there are rooms where you can hop up and down ledges, and one room that connects the cave entrances. The cave has a couple of chests that hold some more items, including a Mind Source.
Split the party
In the next room, you reunite with the rest of the gang. Here, you can basically send some of your friends through the left and right path.
Make sure you try all the forks along the path to pick up the chests. There are some useful items, including a W-Magic materia, Counter materia, Shield materia, and Magic counter materia. When you reach the point where your party splits up, you can send your party members down different paths to get most items. The left and downward path is the one which will allow you to return to the top. The left and upward path is a great one on which to use your Save Crystal to create a save point. It contains the best experience building place in the game. Simply use Elixirs on the Magic Pots and kill them, and you'll net thousands of experience and AP points.
When you reunite with your party and they give you the items they found, only proceed if you're ready to face Sephiroth, and head back and save anyway, as this is the point of no return. If you've edited your save game to get Aeris back in your party, she'll be disappearing for good now.