I have recently joined the ranks of Runescape fanatics. I first tried out the game several years ago. I came back to find massive updates and overhauls. I personally love it, so what there is no PKing. The GE (grand exchange) more than make up for that in my mind.
I have found several places to level for each level group they are:
Levels 3-10
For this particular level range I suggest the goblins to the east of lumbridge. The goblins here are pretty easy and don't hit very hard. The goblins are also found in port Sarim and the goblin village. Another good training monster for this level range is the Al-Kharid warrior which can be found only in Al-Kharid palace. Beware it is very populated and kill stealing is prevalent.
Levels 11-20
This level range, there are two very good places to level. One of them is the barbarian village where barbarians range from 9-29. In the barbarian village there are 4 levels of barbarians for your leveling satisfaction. 9, 10, 15, and 17 there is also Gunthor the brave (level 29). Another area to level in this level bracket is the dwarf's mines where there are levels 7, 10, 11 and also the guards at level 25 for the reckless ones.
Levels 21-35
The two good places to level for this level range are pretty grueling. The first is the town guards at level 21 they will make good cannon fodder. You can find these at the entrances to Varrock and Falador. The other place to level is the stronghold of security. There is Minotaur at level 27.
Levels 36-50
Here there are knights, knights, and….you guessed it more knights. At the white knight's castle in falador there are knights of many levels including 36, 38, 39, and 42. The other knightly place to level is the Black knight's fortress where there is no one there to compete with normally, at level 33 these guys makes good cannon fodder as well.
Levels 51-65
In the caverns south of port Sarim which you go to for the knight's sword quest lay some ice warriors at level 57, they are perfect for this level bracket. Also for this level bracket are the monsters of the Stronghold of security level 3, like the dreaded Catablepon.
Levels 66-99
For the final and obviously hardest range of levels I have devised the Ankou! The ankou are bony ghosts in the last level of the stronghold of security. These monsters range from 75 - 86. Also, for this hard level range I have come up with something predictable, demons. The demons include lesser and greater. Lesser demons at level 82, and greater demons at level 92. These are located in the "Demon Ruins" which are in the 45- 48 wilderness.
That is my synopsis of the f2p leveling guide. I have found these places through lots of quests which are great for levels as well because they usually entail fighting. However the best way to level is just grind it out, or pay to become a member like I didn't.