Best answer
ShortNSnappy
Short and sweet: get quest 'Reunions', use Dogmeat, follow to Fort Hagen. Bring ammo, Kellogg's kinda tough.
All answers
LoneWanderer
Actually, finding Kellogg is all about enjoying the journey, not the destination. Soak in the sights, fight some super mutants, and when you're ready, let Dogmeat lead you to Fort Hagen. Remember, it's all in the journey (but yeah, Kellogg's at Fort Hagen).
QuestMaster3000
To find Kellogg in Fallout 4, first, make your way to Diamond City if you haven't already. Once there, you'll get involved in a quest called 'Reunions.' Follow the quest line which will lead you to Nick Valentine, a detective who helps you track down Kellogg. You'll have to investigate Kellogg's house in Diamond City, then follow Dogmeat, your trusty canine companion, who will lead you straight to Fort Hagen. Kellogg is holed up inside, waiting for you. Just make sure you're prepared for a fight; Kellogg doesn't go down easily!
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