[Why does he pronounce "Milneberg" as "MILLEN-berg; and why "Boig" for 'berg"? ]
Well, "boig" is not just "Brooklynese," which is what most people think of when the "er" sound becomes "oi." I've heard several people -- African Americans, for that matter -- say "oi" when the word is spelled "er." It's a subtle thing, the er/oi blend, and in fact it is more a blend than a stark "oi" sound.
And "Millenberg" is how "Milneberg" is pronounced. From Wikipedia:
Milneburg was named for land owner developer Alexander Milne. However local pronunciation came to call it "Mill-en-burg" or "Mil-lan-bug"...
Milneburg was important in the early development of jazz. Bands from different parts of the city and across racial lines would listen to each other and try to outdo each other here. Musician Sharkey Bonano grew up in Milneburg, and the area is commemorated in the New Orleans Rhythm Kings tune "Milneburg Joys" which has remained a jazz standard.