Kreuzberg? Prenzlauer Berg? Friedrichshain?
 

My girlfriend and I are visiting from New York. We'll be in Berlin for about a week. Aside from all the semi-required touristy stuff, we're interested in staying in a neighborhood convenient walking distance from all sorts of nightlife. We stay up late. As a general rule, we prefer dive-y bars to big clubs, but we definitely want to hit some of the famed techno clubs as well. Berlin has a reputation for parties that go all night and then another night... are the techno clubs the only bars/clubs that stay open past 4AM?

Friedrichshain and Prenzlauer Berg keep popping up as where we should be... what are the pros/cons of both? I've also heard good things about Kreuzberg...?

One thing I've seen in my searches is that they're rather large neighborhoods and to watch out for where you actually get a hotel/hostel/BNB/whatever in either neighborhood as one could end up in a boring or isolated area of the neighborhood...

Based on your bar/nightlife requirements, I'd stay in any one of those areas listed. Prenzlauer Berg may suit you best, but Friedrichshain would also be fine, ditto for Kreuzberg. Wherever you are, there will always be a bar in another part of town worth visiting, so perhaps locate a few bars that suit you and choose accommodation based on that. The U and S-bahns run until 1am-ish, and taxis aren't hard to find or expensive.

One club/complex I will recommend to you is Tacheles - I love going there as it reminds me of how Berlin was pre-Wall coming down, very alternative, independent and a little anarchic. In Prenzlauer Berg, you could start at one end of Schoenhauser Alle (start at Eberswalder Strasse U-Bahn station) and make your way towards Mitte and you'll find bars, clubs, beer gardens, etc to keep you occupied. The Kulturbrauerie on Schoenhauser Alle is great for live music and late nights. Or in Mitte, which is not trendy, but still has some great bars, try Delicious Doughnuts - a bar with great drinks, good vibe and the right side of seedy. Stays open late (around 4am towards the weekend, earlier if it's quiet) and if you arrive after midnight you'll have to be buzzed in.

The madam sure knows her way around.

As OP mentioned, some Berlin districts are pretty huge and have areas where not much is happening.

In Kreuzberg, the "hotspot" would be between Görlitzer Bahnhof and Schlesisches Tor subway stations (U1 line).
In Prenzlauer Berg, it would be around Eberswalder Str. subway station on the U2 line. One subway stop north and south still is good. More north than that gets quieter.
Friedrichshain usually is a bit out of my focus, so I wouldn't really know what to suggest.

All three districts claim to be a bit more on the alternative side. It's more or less still correct for Friedrichshain and Kreuzberg (which are one district now anyway), while Prenzlauer Berg has become more and more gentrified.

Besides the aforementioned clubs, you can TRY to get into Berghain club, near Berlin Ostbahnhof (Eastern railway station). One of the few places that really has a pretty strict door policy.
The Kit Kat Club is a hallmark of Berlin's "anything goes" attitude, but not for the faint of heart. If you as a New Yorker remember the indie movie "Shortbus", it will give you an idea what to expect.

Otherwise, parties often change venues and it's always good to pick up leaflets or flyers in the regular clubs to know where things happen.

If you catch a heat spell, this is a pretty cool place to chill: www.metaxabay.de