Task Set Reward Items (eg: Explorer's ring): Speaking to the Task Masters for the relevant areas while meeting the stat requirements to complete that diary, eg: Bob, Explorer Jack, or Ned for the different tiers of Explorer's ring.
Ectophial: Speaking to Velorina in Port Phasmatys with the requirements for Ghost's Ahoy.
Drakan's Medallian: Burgh de Rott, south of bank in the hole and then searching the coffin while meeting the requirements for Branches of Darkmeyer
Tokkul-Zo: Speaking to the Tzhaar-Mej at the center of the Tzhaar plaza with the requirements for Elder Kiln
Enchanted Lyre: Chopping a branch from the swaying tree west of Relekka, spinning some golden wool from Lalli, and then enchanting the lyre at the Fossegrimen with a raw shark.
Teleport crystal: Killing Elves in Lletya for small elf crystals and then charging them at Arianwynn.
Dramen Staff: Outside the shed in Lumbridge Swamp
Family Gauntlets (Cooking, Goldsmithing, Chaos): Speaking to any of the brothers who give them to you while meeting the requirements for Family Crest
Elemental Shield: Next to the anvil in Seers Village
Fighter Torso / Fighter Hat: Barbarian Assault minigame
Anti-dragon Shield: The Duke in Lumbridge Castle
Wicked Hood: Tam McGrubor in Burthrope
Lit Candle: Ardy Monastery, helpful if you need a light source
Monk's Robes: Upstairs in Edgeville Monastry
Darklight: Ruins of Uzer
Wolfbane Dagger: End of the Mausoleum
Steel Platebody: Middle of the Lava Maze in the Wilderness (good for alching!)
God Capes: Inside the mage bank, go through the sparkling pool and pray to the god statues
Goldsmith Gauntlets: Al-Kharid mine
Salve Amulet (e): North of Abandoned Mine
Defenders: Warriors Guild can be done by getting tokens using your favorite method, and then going upstairs and killing cyclops.
Ava's Devices: Speaking to Ava on the ground floor of Draynor Manor while meeting the requirements for each tier of device.
All RFD gloves are unlocked, and purchasable in the bank chest under Lumby Castle (Up to 100k)
Dragon Scimitar can be purchased inside the Varrock Scimitar Shop (100k)
Empty God Books can be purchased from Jossik, in the tower west of Relleka (1-500 each)
Helm of Neitznot can be purchased on, wait for it, Neitznot (50k)
Initiate and Proselyte Armour can be purchased in Falador Park from Sir Tiffy (20k for the set)
Dragon Dagger can be purchased from Rasolo, south of Baxtorian Falls (20k)
Nature & Law runes are in stock (250 of each) on the second floor of the Mages' Guild (372 for nats, 378 for laws)
Mystic Armor is also in stock on the second floor of the Mages' Guild (235k for the set)
Iban's Staff can be purchased at the entrance of the Underground Pass (100k)