Could you please give me ideas?

I have a few astral quest type runs on my old website, if that helps at all.

Check out: "Glasgow's Personal Astral Quest", "Cloak's Quest for Her Past" and "In the Wake of the Wicked"

Perhaps some of them may help forge a framework for what you need... I do my best to personalise an astral jaunt to both the questors and the plane of choice. Having not yet received my copy of "Street Magic", I don't know how things have changed in 4th...

SR13

alice in wonderland, mirror|mask

What’s the player going there for? Depends on the factors involved like the other poster said. The goal you hope to achieve and type of plain your visiting. Its probably different for the person visiting it too.

The fiery pits of Hell
Silent Hill’s hell world effect
Atlantis
Why not the home of the Greek Gods or something similar.
Valhalla
Labyrinth

Hopefully he wont get lost there and never be able to return.

Conversely, Disney's Hercules is exactly what I would expect to see in a sculpted matrix host, right down to the branding.

But I hate it! I want to kill it and send it back to hell!

How profound are most of those? And what are the trials they go through?

Well, some stories are silly, some are heroic, and some are tragic. You probably don't want too much in the way of silly quests, but here's some suggestions for heroic/tragic quests (some have elements of both heroism and tragedy).

Persephone and Hades: Hermes, god of messengers and other face-types, tries to rescue the goddess of spring from the lord of the dead, but has to end up making a compromise.
Prometheus: This Titan steals fire from the gods for the sake of mankind, and ends up personally suffering for it.
Orpheus: The son of the Muse Calliope uses his beautiful singing voice to try and convince Hades to let his wife Euridyce come back from the dead, but ends up losing her due to his lack of faith.
Cadmus: Cadmus fails to find his kidnapped sister Europa, but ends up killing a dragon and founding the city of Thebes instead. Proof that the Gods never close a door without opening a window.
Perseus and the Gorgon: In this excellent quest, Perseus needed both brains and brawn to slay the foul Medusa. Perseus also manages to rescue his mom from an evil king, kill a sea monster, and bag a hot wife into the bargain.
Heracles/Hercules: After going nuts and killing his wife and children, Heracles is forced to do a bunch of quests for his wimpy cousin, the King of Mycenae, in order to atone for his sins.
Theseus: This prince of Athens goes in the scary Labyrinth and fights the Minotaur.
Oedipus: Oedipus is clever enough to figure out the riddle of the Sphinx, but he can't escape his horrible fate. You may remember Oedipus from the Complex of the same name.
Jason and the Golden Fleece: Jason quests to get the Golden Fleece. Kinda like the Odyssey, but different.

Another good classical tale that unfortunately isn't in D'Aulaires (it's Roman, not Greek) is Cupid and Psyche. This myth is nice if you're designing a quest for a female character, but can be made to work for a male if you switch the genders around.

*smacks 2bit though the Interweb*

How do so many people know about that movie?

One really great example of an astral quest is Michael Moorcock's Fortress of the Pearl.

IIRC, the adventure module Harlequin's Back is one ginormous metaplanar quest. You can always check that out.

Also keep in mind that astral quests don't have to make sense... they can be very symbolic. If they are going on the quest to find something in particular (an item or a spirit's true name, etc) make the quest symbolic of the ideology of the item they pursue.

If they are using a quest as an initiation rite, then make the quest symbolic of a challenge (fighting a powerful spirit, scaling a mountain, etc). If they are shamanic, you can have their totem issue them a series of tests to show their worthiness (Wolf has them hunt using only their natural gifts, Obatala challenges him to quell a riot, etc)

I like my quests to have a "theme"... whether the player recognizes that theme or not is not important. In my game "In the Wake of the Wicked" my players didn't realize that they were bringing out the spirit of Jack the Ripper...they ignored the signs. They paid for it later.

SR13

Had my players go on an astral quest in SR3 that could easily be used in SR4. Basically, they were attacking a BBEG from Winternight in the cult's own toxic stronghold in French Guiana (never said they were bright). The BBEG pointed at one of his two bound-by-truename free spirits of the sky, Muninn (they had already taken out Huginn), and commanded "eliminate them from the face of the Earth". The spirit then used Astral Gateway to send them to the metaplanes, while he made it appear that their bodies were destroyed.

Once in the metaplanes, in a realm which appeared as Asgard (and other realms of the World Tree), he appeared in raven form told them that he was bound by his truename, which appeared in the realms as an orichalcum band around it's ankle. In order to ever return to Midgard (the real world), they would have to undertake a Quest -- by combining various components found in the realms, they could have the Norse dwarf-smiths create a set of magical snipping shears that can break any bond. Upon being freed, Muninn would not only escort them back to their bodies, but aid them in defeating the BBEG.

Of course, it's never so easy, as they needed the heart of fire, the bone of death, the thread of life, the tears of hell, the broken chain, and the blind man's sight...

Oh, and all cyber was transformed into magical items in Norse fashion, in that every item had a Name and various powers -- I think even Odin's chamber pot had it's own Name... All of their abilities were also translated -- the sammie had some deadly sword-fu, the sniper became an archer, the rigger became a beastmaster, the decker/face could hack the weaves of Fate, the mage could do some Nordic seidhr-magick, and so on...

It was fun times for all, and they even came up with a nickname for the alternate Asgardian adventures -- ShadowRUNE...