Good idea with the Lucid School Wissam 
I have a new ques suggestion
Find your Inner Child.
ince Painocus suggested to find the name of your dreamworld, I have a variation for that theme, ask a DC what your name is, and see if he/she answers your regular name or something unusual 
I have a new suggestion:
Merge with a DC.
So that
you + DC = one new person
This person will of course have all your memories(both the DC’s memories and your memorys)
but he/she will be a whole other person.
Suggestion: Finding hidden/lost parts of yourself
Not phisically, but something like attribute of personality or a dreams, lost by accidents or by time passing by. Could be materialized by feeling, a thing, or DC.
i didn’t have time to read through this thread but i’d suggest writing a story IRL where the main character does everything that you want to do in a LD, then when u get a LD put yourself in the story.
What about expanding things that you would normal have to get a microscope to look at (such as atoms) and seeing if their physical properties are any different than the models in science classes (if this makes any sense).
One thing that I’ve been planning on doing the next time I have a vivid LD is go on an epic quest to find a special music box. When you open it, it plays beautiful (hopefully original) music. I haven’t exactly thought up the specifics, but it should be an interesting expiriment.
Something I strive to do and think would be interesting would be to map out your mind as a physical place, be it a building, a city, or even a planet. Explore the Caves of the Subconscious or even take a literal trip down Memory Lane.
I just thought of a good idea. For all you music players - why don’t you play with your instruments and try to create music that becomes alive?
I’d like to see the results if someone tried those and normally doesnt play an instrument.
Find out what your Daemon looks like and it’s name.
For those who haven’t read Pullman’s books.
A Daemon is part of your soul, represented by a talking animal,
in most cases of the opposite sex.
While you are a child they daemon can change shape all the time but when you grow up it will lost the abilty to change and became one animal representing you for the rest of your life.
The Daemon is a really good one, I’d do that. In fact, I’ll probably do it even if it’s not a quest.
Elemental quest - Play with the elements! Fire, Water, Air, Earth and Aether (AKA Spirit). See what you like best, etc. We can consider also different philosophies on the elements, such as the Chinese one, with Metal and Wood 
-Rearrange the galaxy! Don’t you hate Neptune being so far away? Just push it closer to the sun and enjoy the view from earth!
That’s what I did last night. I accidently burnt Uranus to a crisp, Venus and Neptune crashed into eachother and the gasses destroyed the earth…
-Alchemy, Fullmetal Alchemist style! Clap your hands together and touch the molecules you want to rearrange!
I built a house this way. And I made a tree grow, but the tree became too big and blocked out the sun. All the DCs died. Whoops…
-To the center of the earth! Drop through the floor, all the way to the centre of the earth, keep falling and come up again on the other side.
Fun, but molten rocks hurt!
-Play sports with DC’s!
Just make sure they don’t fall off their brooms…
for those people who like board games and adventure:
play Jumanji.(remember the movie Jumanji)
Make someone believe that he is just a character in your dream! I tried it, but they just gave me weird looks… Maybe you will have more luck.
How about meeting up with a deceased friend, relative or pet. I often dream of my grandparents, and my deceased cat who passed away a year and a half ago 
. Unfortunately, I rarely become lucid when I dream of them. I would love to hold my cat again
He lived to the ripe old age of 18!
10 random suggestions off the top of my head:
Animorph
Take lsd
Go back in time\forward in time. (eg: See what your life’s like in 10 years or something)
Sit on a cloud.
Make everything upside down
Take your skin off and walk round the town centre.
Eat anything and everything. yes everything. eg: shoe, mobile phone, even vegatbales.
Hear through your nose, speak through your ears, see through your mouth and taste with your eyes.
Jump across roofs.
Go to the bottom of the ocean.
Cook something.
Well I think this would be really, really, unbelievably hard, so not that much help maybe - turn your body into a swarm of bees.
Basically try to control lots and lots of bodies with one mind. I also think it would be interesting to do it with bees because they have useless individual bodies and that will make it interesting to see how we will cope when we to do normal things.
My suggestion:
Poke a Tiger in the eye!
Or you could hug one 
Or go on Safari and do the above too!
Fleep
Try and see colors you can’t imagine.
Ok that is a paradox, I mean try and see colors you can’t imagine in waking life.
Try that not only with colors but with sounds, feelings, taste, and things.