I got another one, participate in a Mario Kart-esque race.Describe what the track, the other racers,the weapons, and the cars look like.Also who wins.
Cook your favorite meal (or order it at a restaurant) and see what it tastes like in a dream.
Rip the fabric of Spacetime.
… Of course the fabric would repair itself in my dream world. I believe in string theory. 
Jump into a painting, and live in the world drawn in the painting. 
Oh I could imagine stepping into a painting of a large flower field on a cliff with a wonderful ocean view, at sunset. I’d spawn myself a throne and sit there for the entire dream, taking in the senses, smelling the sea, feeling the gentle sea breeze…
This really inspires the LD inspiration vibes inside me. Now if only I could find a way to inspire the programming ones.
SPOILER - Click to view
I hope the painting one gets picked 
How about… Meet with Stephen LaBerge in a Lucid Dream? 
Potential tasks could be:
-Talk to him about LDs.
-See if he has any advice for you.
-Demonstrate your ability to control the envrionment to him and see what he has to say about it.
Etc.
Use Neo’s super abilities from the matrix-trilogy!
For example:
- visit a special location (like a subway station) and make remarkable kung-fu-jumps over the entire place
- fight against the computer agent Smith
- make beats and fight actions in fast motion
- jump over the distance between two skyscraper
- avoid bullets in slow motion
- see the whole world in cryptical green signs
- use phones the change into another world or to wake up
BECOME a planet.
What about a Lucid TV Show?
Go into a dream and make a show from everything in your dream,
talk to DCs, examine the trueness of your Dream, or just travel though Worlds in front of the Camera, and being camera shy isnt a problem. It`s your own dream.
Dream Potion
Umm… Maybe make/buy/find a vial or a beaker-something that can hold liquids. Then go throughout your house(or wherever you happen to be) and put things in it, kind of like a potion. Then mix it all together and drink it. See what sort of interesting things happen 
My idea is to go into someones dream and make them lucid, if shared dreaming is possible. also, you can be a nightmare buster, so if they are having a nightmare, well, bust it! NIGHTMARE BUSTERS! (got the urge… sorry LOL) you can also summon your friend from they’re dream, and tell them it’s a dream and have fun with them. well good luck if this becomes a quest
Ask a DC a question about something that you wouldn’t know the answer to in RL, later when you wake up, look up the answer and see if your DC was right.
Step into your shadow! I got this idea from a song.
[spoiler]…
“See my shadow changing,
Stretching up and over me.
Soften this old armor.
Hoping I can clear the way
By stepping through my shadow,
Coming out the other side.
Step into the shadow.
Forty six and two are just ahead of me.”
…
Tool - Forty Six & 2
(Yeah, I can’t stop listening to Tool. 
)[/spoiler]
The idea, I guess, is kinda like to meet your dark side, confront it, embrace it, whatever, to grow and evolve.
The shadow can be used as a portal, just like we use mirrors 
See where you end up!
Anyway, other ideas also involving your shadow: Talk to it, interact with it (waving or other gestures), grab it, shake hands, hug it, the list goes on
You should look up the books by Sergej Lukianenko.
There the “Others” , who are some sort of people with unnatural powers, step into their shadows to get inside of a parallele-world they call “the Twilight” there are also several layers of this twilight, and the more powerful of the “Others” can change between them… aaam ok its hard to tell. But I can only recommend these books. A mixture of fantasy, original ideas and a bit soft-horror
Yeah. Sorry for being offtopic
I have been having this idea the last few days - its a way of trying to test your cognitive memory whilst in a lucid dream.
Basically, when we remember our dreams its when we are awake - we do so by making a conscious effort (sometimes not so conscious) to do so. What if, we try to bring back memories from waking life into the dream? Describe how you see your waking life reality in your dream reality - then you really do have two realities and you can be lucid in both of them!
I am sure there is some logic there… but I dont think I have expressed the idea very well!? 
Some of my ideas…
-Look for the invisible door & open it
-Go to the Lucid Dreaming Convention! -Watch presentations, meet people, browse around.
-Lucid Cooking! -Throw everything you can into a pot, turn up the heat and see what you cook up. 
-Go into a black hole -probably listed already?
-Shrink and travel in a random DC’s insides.
-Fuse the Sun&Moon together by force or whatever way possible, observe the effects towards Earth. (or you can fuse planets) 
That is all for nows!
I have a challange if it hasnt been done allready… Lets try space travel. we could go to a distant planet, or the moon. Or a black hole what do you think?
Split from the Quest topic.
Meet your past or future selves while flying!
I’m all for going to Pandora from Avatar!!!
4 ideas.
Stunt driving.
See the inside of a technical object, like an xbox 360 or a pc.
Make a new instrument.
Oh, a nd wouldn’t it be cool to just draw a door with chalk out of nowhere and go through it! Or use the chalk to draw anything and make it come alive! WOAH!
Change the dominant population of the world.
Go back to the past, a point when humans were still on the same intelligence level as other animals. Influence a certain species to make them smarter than man. Travel forward to the early 21st century to see how the new species changed the world. Better or worse, you decide.