You can complete the "Recruitment Drive" quest, that lets you get your respawn point to Falador.
You can complete the "Kings Ransom" quest you unlock the "Knight Waves Training" mini-game ( hard-ish ), this will let you set your respawn point to Camelot.
Finish the quest Desert treasure and your home teleport will be Edgeville,
you have to do the plague city quest then you can teleport there if not you have to take the long way and walk '.'
The "Desert Treasure" quest, this gives you access to the Ancient Magicks spellbook, of which has the spell "Kharyll Teleport" which teleports you to Canfis Pub.
Some can be random events, they take you to a certain place, where you doing something and then they take you back, usually followed by a reward.
It's currently not possible to undo a quest in RuneScape.
The legends quest on runescape is not gone, I suggest that you check again.
You can use a camelot teleport and walk south-east and you will arrive in Catherby. This is the fastest way I know of.
To get a pet dog on Runescape you will need to complete the "Wolf Whistle" Quest which in turn, unlocks "Summoning" skill, then head on to Yanillle ( you can get there almost quickly by watchtower teleport of ring of dueling to "Castle Wars", then go to pet shop there to buy a dog, bring around 5000gp, shouldn't be that much, but just in case.P.S The "Wolf Whistle" quest is fairly easy.
A quest on Runescape is an adventure that puts you in a conflict, you solve it and you get rewards like money, skill experience points, quest points, and items.
if you are talking about the Christmas Quest than go either to the wizards tower or to a snow imp wearing a santa hat once your there click on him and ask if he can teleport you. Once you are at the um place slide on the ice to get to a cave entrance (if you look on the minimap it's where all the people are that are not on the ice) go in now go to youtube and look up Runescape Christmas Quest Solution 2008 and do what he does.
If you quit runescape...
There are many websites where one can get advice on completing a Runescape quest. The Runescape website itself offers advice as does the website Tip.It.