You will visit the city of Concord during the first main quest - Out of Time. There are many buildings here, but you won't be able to enter most of them. On the border of the city you will face some bloodbugs. Additionally, during the first visit to the city you will have to eliminate many bandits.
You will find a fusion core in the city's underground. However, you will be able to get there only once you defeat the Deathclaw
In the building named Concord Speakeasy you will find a safe with advanced security. Inside you will find some weaponry and the Stealth Boy that makes you temporarily invisible. In the same building you will find a door secured with advanced lock. Inside you will find some weapons.
In few points of the city you will find entrances to the sewers. In the tunnel complex you will find many interesting items, but you must watch out for enemies.