Combat
There are heaps of places you can train combat. A great place is the Edgeville dungeons. You go to Edgeville and go into the room with all the coffins. Then, go down the ladder. In the dungeons there are heaps of monsters for a whole range of levels. From level 3 rats to level 172 black demons!
Ranged and Magic
One of the benefits of these two skills is that you don't always have to be hit back. For example, if you range or mage a monster behind a cage it can't hit back at you! This means that you can train on whatever level monster you like and you will never die. There are lots of places, I would suggest the Lesser Demon in the top floor of the Wizards Tower. There are also caged monsters in the jail in Port Sarim. If you get to level 33 magic you can use telekinetic grab to "grab" the items that the monsters drop even if they are behind a cage.
Prayer
I would suggest going into the Edgeville dungeons to where the Hillgiants are. They drop big bones that you can bury. If you don't want to go there you can also go to one of the chicken pens. You can run around picking up the bones that other people have left behind or you could kill them yourself.
Mining
I would go to the dwarven mines. If you want to bank the ores you mine there is a ladder that goes straight up to Falador, but you have to run through the scorpians. I would suggest, however, just dropping the ores for the fastest training. You can mine tin and copper until you can mine iron. Then mine iron until you are level 60 and can get into the mining guild.
Smithing
If you have the money I would suggest buying bars at Varrock bank and smithing them at the anvils near by. Or, you could mine ores in Dwarven mine and smelt them in Fally and then go back to the Dwarven mines to smith them.
Cooking
If you have the money I would go to Port Sarim and go to the fishing shop and buy fish and cook them. Or, you could go to Draynor and fish for shrimps or whatever you want there. You could also go to the chicken pen and cook the chickens on the ground.
Crafting
You could mine for clay in the dwarven mines and then use it with the pottery wheel in Barbarian village. Or you could kill cows and collect their hides in the cow pen near Al Kharid, then take them to the tanner in Al Kharid. It is best if you complet the Prince Ali quest so you don't have to pay for entry into Al Kharid for this.
Firemaking
There is no best spot to train firemaking. And, if you think about it, firemaking is a fairly useless skill. However, if you do want to train it go to a place with lots of trees or you could buy your logs from the general store of from another player.
Fishing
There are a lot of places to train fishing. Start at Draynor and net shrimps until you can fish with a rod. When you can fish lobsters go to Karamja.
Runecrafting
Depending on what rune you want to craft there are many different places. You could either mine for rune ess or buy it from other players. There are some monsters that drop noted rune essence as well. For example the minotaur in the Stronghold of Security drops 5-15 noted essence. Then, you should go to south of fally to the Air altar and then you can just go north to the bank to bank your runes.
Woodcutting
Woodcutting is pretty easy. Just anywhere with trees! Which is pretty much anywhere. Also, if you want to sell them you will want it to be close to a bank.
I hope this guide will help you in your quest to become a skilled player of Runescape. Have fun!
Thanx