Once you have come to the end of destiny 2's campaign you will find vendors scattered around the various worlds which will gift and sell you things. Below is a list of these vendors, where you can expect to find them, what they sell, and how to level them up.
Cayde-6, Vanguard Scout
Tower Hanger
Cayde-6 will sell you two items that can be used on Patrol. The first is Treasure Maps which highlights the locations of chests in that given week's Flashpoint location and the second is Scout Reports which is a consumable that enables you to farm easily as it highlights chests in a specific area for the next four hours.
Amanda Holliday, Chief Shipwright
Tower Hanger
Amanda Holliday can be found alongside Cayde-6 at the Tower hanger. She will sell you basic ships and vehicles. Note: The Sparrows she sells are not fast.
Tess Everis, Eververse Trading Co.
Tower Courtyard
Tess Everus deals in microtransactions for destiny 2 which involves spending real money on Silver which is a currency that enables you to purchase packs of Bright Engrams. She will also decrypt Bright Engrams for you.
Kadi 55-30 and Darbi 55-30, Postmasters
Tower Courtyard and The Farm
Kadi 55-30 can be found in the Tower Courtyard and Darbi 55-30 can be found on The Farm. Both of these Postmasters will keep hold of any loot that you missed along the way. Note: To collect your loot just walk up to them.
Commander Zavala, Vanguard Tactical
Tower Courtyard
Commander Zavala will offer you rewards for Strike missions in the form of Vanguard tokens which will net you loot each time you level up. He will also give you access to the nightfall Strike that gives you the opportunity to earn better rewards.
Lord Shaxx, The Crucible
Tower Courtyard and The Farm
Lord Shaxx is the overseer of the Crucible. Completing Crucible matches will net you Crucible tokens which if you then take to Lord Shaxx will earn you rewards.
Arcite 99-40, Crucible Gunsmith
The Farm
During the early stages of destiny 2 you will find Arcite 99-40 at The Farm and he will sell you power appropriate equipment. Once you have completed the campaign and unlocked the Tower he will disappear entirely as a vendor.
Master Rahool, Cryptarch
Tower Courtyard
Master Rahool is the Cryptarch for destiny 2. Whenever you get an exotic or Legendary Engram he will turn it into equipment.
Tyra Karn, Cryptarch
The Farm
Tyra Karn functions the same as Master Rahool, she will decrypt any Engram you give her.
Banshee-44, Gunsmith
Tower Courtyard
Banshee-44 can be found in a booth just off to the side of the Tower courtyard and you can turn in items to him in exchange for loot. When you have given him enough Gunsmith Materials from dismantling equipment that is Rare or above he will give you a Legendary weapon. Banshee-44 will also sell you mods for Glimmer and Mod Components which can modify your equipment.
Ikora Rey, Vanguard Research
Tower Bazaar
Talking to Ikora Rey will enable you to replay old story missions and select one of three weekly missions where upon completion will earn you Vanguard Research tokens which she will exchange for loot.
Suraya Hawthorne, Clan Steward
Tower Bazaar
Suraya Hawthorne will sell you some 200-power equipment in exchange for some Glimmer. She will also give you powerful equipment in exchange for any Clan Experience you earned from Clan activities.
Devrim Kay, Dead Zone scout
European Dead Zone (EDZ)
Devrim Kay can be found at the church in the European Dead Zone's Trostland. He wll sell you loot and exchange any EDZ tokens you earn for Legendary equipment. Devrim Kay also sells green quality gear that caps out at 200 power.
Sloane, Field Commander
Siren's Watch on Titan
Sloane will sell you 200-power green gear as well as trade Legendary loot for Arcology tokens. Like other vendors you can use the tokens you gain from completing Public Events and doing other activities on Titan to level up Sloane. Whenever she levels up she will gift you high level equipment.
Failsafe, Exodus Black AI
Exodus Black on Nessus
Exodus Black AI Failsafe is more often than not a friendly AI who will give you equipment. You can offer up Nessus tokens to her for Legendary loot or buy her 200-power green gear for Glimmer.
Asher Mir, Fragmented Researcher
Lo
Located near Rupture on Lo Fragmented Researcher Asher Mir is the last planetary vendor you will meet. Like the others, he will sell you power level 200 green gear as well as trade Io tokens for Legendary items.
Xur, Agent of the Nine
This vendor represents the Order of the Nine, he appears weekly to sell you exotic-level equipment in exchange for legendary shards.