Vannaka can be found in the Edgeville dungeon, just east of the Wilderness gate. He will give you Slayer tasks of 'medium' difficulty to complete, and you must be at least level 40 Combat or higher.
Vannaka's Possible Assignments
Monster Where to Find
Aberrant Specter Canifis Slayer Tower
Bloodvelds Canifis Slayer Tower
Blue Dragons Taverley Dungeon, Heroes Guild
Crawling Hands Canifis Slayer Tower
Crocodile Elid River, west of Nardah
Dagannoths Lighthouse west of Rellekka
Desert Lizards Kharidian Desert
Earth Warriors Edgeville Wilderness Dungeon
Elves Tirannwn Elf Camp
Fire Giants Waterfall
Ghouls Northwest of the Mort Myre Swamp
Green Dragons Wilderness
Hellhounds Ardougne Dungeon, Taverley Dungeon
Hill Giants Edgeville Dungeon, Wilderness
Ice Giants Port Sarim Ice Cavern, Wolf Mountain Cave
Ice Warriors Port Sarim Ice Cavern
Kalphites Kalphite Dungeon
Lesser Demons Karamja Volcano, Taverley Dungeon
Molanisk Dorgesh-Kaan
Moss Giants Varrock Sewer, Wilderness
Ogres Feldip Hills, Tree Gnome Village Cavern
Otherworldly Beings Lost City of Zanaris
Pyre Fiends Fremennik Slayer Caves
Rock Slugs Fremennik Slayer Caves
Trolls Mountain Northwest of Burthorpe
Turoths Fremennik Slayer Caves
Vampires Swamp east of Canifis
Werewolves Canifis
Chaeldar
Chaeldar can be found just south of the entrance to the Lost City of Zanaris. You need to equip your Dramen Staff from the Lost City Quest and enter the small shack in the Lumbridge Swamp to be teleported to the Lost City. You can also use the Fairy Ring in the Morytania Woods to get there. Chaeldar gives more difficult tasks, and for this reason he requires at least level 70 Combat.
Chaeldar's Possible Assignments
Monster Where to Find
Banshees Canifis Slayer Tower
Basilisks Fremennik Slayer Caves
Brine Rat Brine Rat Caves
Blue Dragons Taverley Dungeon, Heroes Guild
Bronze Dragons Brimhaven Dungeon
Cave Crawlers Fremennik Slayer Caves
Cave Horrors Mos Le'Harmless Caves
Cockatrices Fremennik Slayer Caves
Crawling Hands Canifis Slayer Tower
Dagannoths Lighthouse west of Rellekka
Elves Isafdar Woods
Fire Giants Waterfall
Greater Demons Entrana Dungeon, Brimhaven Dungeon, Ogre Enclave, Lava Maze Dungeon, Wilderness Demonic Ruins
Harpie Bug Swarms West of Tai Bwo Wannai, near Jogre Caves.
Hellhounds Ardougne Dungeon, Taverley Dungeon
Infernal Mages Canifis Slayer Dungeon
Iron Dragons Brimhaven Dungeon
Jellies Fremennik Slayer Caves
Jungle Horrors Mos Le'Harmless
Kalphites Kalphite Dungeon
Lesser Demons Karamja Volcano
Molanisks Dorgesh-Kaan South Dungeon
Pyre Fiends Fremennik Slayer Caves
Shadow Warriors Legend's Guild Dungeon
Steel Dragons Brimhaven Dungeon
Trolls Death Plateau
Turoths Fremennik Slayer Caves
Wall Beasts Lumbridge Slayer Dungeon
Zygomites Lost City of Zanaris
Duradel