Not a dumb question, but there's a difference between a 4 a.m. license and a 4 a.m. last call. The license means the legal limit for serving, not a promise you can walk in at 3:50 and order a drink. A bar that stays open until 4 has already done last call earlier—anywhere from 3:15 to 3:55, depending on the owner, block, and how much noise pressure they get from neighbors or the community board.
In my experience, Manhattan side streets in the East Village used to push later, but a lot of places have tightened up. You'll see the 3:15–3:30 hard stop at spots with more foot traffic or hostel/bar-crawl crowds, especially Friday and Saturday. The places that pour at 3:50 are usually quieter, with the same bartender and mostly regulars. I've been in a place on Avenue B where the bartender announced last call at 3:25 and collected glasses at 3:45, and another around 7th Street that poured a last beer at 3:50 if you were seated and already on a tab.
If you're trying to avoid being the late guy, show up by 2:30. Treat anything after 3:30 as bonus time. Also, a locked door at 3:15 doesn't mean the block closes early; it usually means that particular bar's house policy or capacity setup. Always watch for the 'lights on' signal—that's the real end.