Where does Kirito get his new gear? In the beginning of the Sword Art Online anime, episode 2 "Beater", Kirito acquires the Coat of Midnight when getting the last attack bonus on the boss.

Up until episode 7, "Warmth of the Heart", it appears he is using mostly the same gear. In the beginning of this episode when we first see him, he is daunting a new coat and his Elucidator sword. Lizbeth does say, "this is the gnarliest sword you can get from a monster drop" or something to that effect. 

Is there ever any mention of where/how he acquired his new gear? I haven't read the manga series, is there any mention in it?
The Elucidator was a drop from "a boss" on the 50th Floor. It's not really specified which boss dropped it though, as it could have been the main Floor Boss, a Field Boss, or maybe a boss in a dungeon that happened to be on the 50th Floor. At the time he got it, the sword still had too high of a requirement for him to even wield, but he still consistently upgraded it.

Kirito's coat also changes between most episodes (until they stop changing in Episode 7) and most of his coats are probably either drops, or tailored. However, it's stated that Kirito's final coat, the Blackwyrm Coat, was crafted by a player called Ashley, which was referred to him by Asuna, during the murder mystery story—though that part was cut out of the anime.