There are a variety of weapons available from both side quests and faction quests, depending on your allegiances in the game and how thoroughly you clear out the side quests it's quite easy to miss many. This list doesn't include weapons you may find as a result of murdering friendlies (for example killing Virgil to get Virgil's rifle).
Side quests
Below is the list of items directly available as a result of quests:
- Agatha’s Dress, reward for completing Curtain Call as a female
- Ashmaker Minigun, potential reward for completing Big Dig
- Broadsider, potential reward for completing Last Voyage of the USS Constitution
- Captain Ironsides’ Hat, potential reward for completing Last Voyage of the USS Constitution
- Eddie's Peace .44 Pistol, found during the quest Long Time Coming
- Lorenzo's Artifact Gamma Gun, reward for completing The Secret of Cabot House
- Reba II Hunting Rifle, potential reward for completing Barney Rock
- Reginald’s Suit, reward for completing Curtain Call as a male
- Shem Drowne Sword, reward for completing The Gilded Grasshopper
- Silver Shroud Armor, reward for completing The Silver Shroud
- Silver Shroud Hat, reward for completing The Silver Shroud
- Silver Submachine Gun, reward for completing The Silver Shroud
In addition to the above list, there are a variety of instances throughout the game where as a result of your actions a NPC vendor will become hostile to you. Such examples include the Battle of Bunker Hill resulting in the deaths of vendor NPCs like Deb, and Human Error resulting in the citizens of Covenant becoming hostile you, like Penny Fitzgerald. I'm not going to include Diamond City or Goodneighbor in this list because if you become hostile to them that's your own fault!
Sold by Deb in Bunker Hill
- Destroyer's left arm
- Black Ops Chestpiece
- Black Ops Right Shinguard
Sold by Penny in Covenant
Brotherhood of Steel quests
With the exception of Righteous Authority, all of the weapons below require progression through the Brotherhood of Steel quest line to the point where you have access to the Prydwen, and then some more require you to hold a particular rank within the Brotherhood.
Needless to say, if you become hostile to the Brotherhood of Steel you will lose access to this faction's vendors.
- AX90 Fury Plasma Rifle, sold on the Prydwen
- Exemplar’s T-60c Torso, reward for completing Duty of Dishonor by persuading Clarke to turn himself in
- Righteous Authority Laser Rifle, quest reward for completing Call to Arms
- Steadfast BOS Combat Armor Chest Piece, potential quest reward for completing The Lost Patrol
- Survivor's Special Laser Rifle, potential quest reward for completing The Lost Patrol
- Visionary’s T-60c Helm, for completing A Loose End
Requisitioned from Teagan
- Commando Chest Piece
- Commando Helmet
- Death From Above Missile Launcher, sold by Teagan after reaching the rank of Paladin
- Honor
- Sentinel's Plasmacaster Plasma Thrower, sold by Teagan on the Prydwen after reaching the rank of Sentinel
- Vengeance
Minutemen quests
The Minutemen don't really have anything all that special, certainly not before taking back the Castle but then you do get access to a Gauss Rifle...
- The Last Minute Gauss Rifle, sold at the Castle after completing Old Guns from Ronnie
Railroad quests
I haven't included the Railway Rifle in this list as it is possible to find this elsewhere, but the Railway Rifle can be a possible quest reward for completing Underground Undercover. Failing that you can head over to Big John's Salvage for a guaranteed spawn.
Needless to say, if you become hostile to the Railroad you will lose access to this faction's vendors.
- Deliverer 10mm Pistol, reward for completing Tradecraft
- Final Judgement Gatling Laser, carried by Elder Maxson during Precipice of War
- Tinker Tom Special Hunting Rifle, sold by Tinker Tom in the Railroad HQ
Institute quests
The super powerful Experiment 18A is available very early on in the Institute quest line, you can pick it up immediately after speaking to each of the department heads before you first leave the Institute. The Wazer Wifle is an end game weapon only available after completing three unmarked quests to fetch items from the wasteland.
Needless to say, if you become hostile to the Institute you will lose access to this faction's vendors.
- Final Judgement Gatling Laser, carried by Elder Maxson during Airship Down
- Liam’s Glasses, reward for completing Plugging a Leak
- Wazer Wifle Laser Rifle, reward for completing Shaun's quest line
From Institute requisitions
- Experiment 18A
- Mark 2 Synth Chest Piece
- Mark 2 Synth Helmet
- Mark 3 Synth Chest Piece
- Mark 3 Synth Right Arm
- Mark 4 Synth Chest Piece
- Mark 4 Synth Left Leg
Best Answer
Looks like you finished the main story line. What Maxson refers to is the quests given by paladin Danse's team. You could try to add mods to your game to track down the quests that you are missing or change the gameplay.
If you finished all the quests, you may want to fix some objectives for yourself like chasing all the unique monsters and deathclaws, gathering power armors, exploring vaults, building huge settlements or trying new perks.
Last but not least, you should consider exploring the sea bottom and the irradiated area in the south.
If this is not enough, all that's left to do is to buy a DLC