Berlin Advice? First time going there.

Plenty of prior questions on this topic - https://search.ricksteves.com/?button=&filter=Travel+Forum&query=first+time+berlin&utf8=%E2%9C%93 You can easily fill many days with activities just in Berlin without day trips (I spent 5 nights and never left the city).

Re: flights, yes open jaw/multi city flights would be best. You have plenty of options from NYC area, including some direct flights to Berlin. Just make sure your Krakow return flight has a decent layover on the way back.

Berlin is a large city by area, there is really no area that is the best for "enabling reasonably easy visits to the sites". It depends a bit on what kind of sites you are looking for, but in general the popular tourist sites are spread out all over the city. And while you can cover a lot by walking, you will need to use the public transportation network to get around.

For cold war sites, the wall memorial is probably a must. Regarding day trips, Potsdam is a good option.

Rick's top sightseeing picks for Berlin can be found on this website:

Berlin sightseeing << Click on "At a Glance"

Rick's brief descriptions will allow you to determine which sights are WWII- or Cold War-related. Despite spending six full days in the city, I still didn't get to some important places like the German History Museum. You'll need to be very selective.

In addition to the spots on Rick's list, I enjoyed these two:

Tranenpalast

Gedenkstatte Berlin-Hohenschoenhausen

The Tranenpalast was as Cold War crossing point used during the years when Berlin was divided. It has museum-like displays highlighting the emotional impact of the division of the city.

The Berlin-Hohenschoenhausen Memorial has been established in a former secret-police prison and interrogation center. Tours are offered in English. There's also a modest-sized museum that covers some of the same information imparted on the tour, so if you are able to take the tour, the museum can probably be skipped. This is located well outside the center of Berlin. As of 2015 it required a tram ride and a bit of a walk. Although I found it very interesting, on a short visit to the city I might skip it since there are so many more-conveniently-located places to go.

I'd choose whichever airline has the best fare and schedule. That said, the two most physically uncomfortable airplane seats I've ever been subjected to were both on Lufthansa planes; unfortunately, one of those trips was transatlantic. I've only flown LOT once, on a flight from Odesa to Warsaw; that flight was fine.

Berlin is huge and spread out. You will almost certainly need to take public transportation at some point. Make a list of of the WWII/Cold War sites you're interested in. I did this in Google Maps - look up a place you want to see, click "save" under the description, and it should prompt you to add it to a list of saves, or to create a new list. Once you've added what you want to see, you can look at your map of saves and plan your sightseeing - so that you don't waste valuable time going back and forth across the city unecessarily.
I have been to Berlin four times and there are still historical sights I haven't seen. Treptower Park! The Stasi Museum! Sachsenhausen! Next time...
For a first timer, I'd recommend the Reichstag (reservation required), East Side Gallery, Topography of Terror, the Wall memorial, the Tiergarten (where there is a Russian war memorial) Tranenpalast, and maybe a trip to Potsdam if you have enough time. I really enjoyed Cecilienhof, where the Potsdam Conference was held. You can ride the train or S-Bahn to Potsdam, then transfer to the bus which will let you out on the Bridge of Spies. You can see that, then use Google Maps to guide you on a walk through a pretty neighborhood to Cecilienhof.
The Rick Steves Europe audioguide app has a nice walking tour of Berlin that starts at the Reichstag and ends up, I think, near the TV Tower. It's about an hour and a half, gives a nice historical overview, and you hit a bunch of sites right there close together.

Can't recommend any specific central hotels, as I usually stay in Air BnB, but staying in Hackescher Markt or anywhere in Mitte will be central to transport links to anywhere you want to go.

I am fond of the Motel One chain and they have one near the main train station, which makes it easy to go on other trips.

My recommendation is to do a good walking tour your 1st day, so you have some orientation to the city as well as some context to and history to match the landmarks you are seeing. My go to tour company there is "Insider Tours".

Some sites that might be of interest that others have not mentioned yet, would be Track 17, the Olympic Stadium, and Wannsee Villa. I know you said you were going to Auschwitz, but Ravensbrück may be quite different. It was for women. Lots of resistance fighters from countries all around Europe, spies, Jehovah Witnesses, and so many more. The Soviets used this KZ and Sachsenhausen after WW2.

Side trip to Potsdam, a cruise through the Spree Forest, are some other activities to do.

I think Hackescher Markt is the most central location.

I second the rec for Hackescher Markt. I stayed at the Adina Apartment Hotel Hackescher Markt in the Hackescher Markt area. My room was a studio since I was by myself but they also have 1-2 bedroom apartments with fully equipped kitchens, washer and dryer and so on. They do have hotels in other Berlin locations as well, but I personally really liked this location. The staff was friendly and courteous, and the rooms were very well prepared, large, clean and nice. Breakfast is available although given the kitchen facilities, I just ate in my room in the morning.

Also, the hotel is very convenient to the U-Bahn, S-Bahn, and trams, and is an easy walk to the major museums. The DDR museum is only a few blocks away along and Museum Island is a quick 5 minute walk. There are several grocery stores a few blocks away along with a couple of wine shops and many really good restaurants. I would definitely stay in this location again.

FWIW, I also stayed at the Motel One mentioned by Ms. Jo. I did like that hotel as it was clean and reasonably priced and very close to the train station. However, I preferred the Hackescher Markt area as I found it a bit more walkable and closer to a lot of the sights. I also felt more comfortable walking through the area at night, and as I mentioned, there were quite a few good restaurants nearby. I felt like Hackescher Markt had a nicer ambience than the Motel One area (imo).

To each one of you who has responded to my query, a sincere thank you! You have all certainly given me great suggestions, both as to lodging and to sights to see. Much to consider as I continue my planning. The suggestions are making me think I might need to add a day or two. And the directions to other sites on the RS website are appreciated. Lots of useful info. And so, another thank you. 😊😊

There's a lot to see in Berlin, as others have noted. Eight days was about right for me, but my interests included the museums on Museum Island, which aren't about 20th century history. The German History Museum is supposed to be excellent, but is closed for several years -- not sure when it will reopen but probably well after your planned visit.

I'd recommend a tour with Original Berlin Walks, which has a good reputation. And I second Mardee's recommendation of the Adina Hotel at Hackescher Markt. You can get there on the S-Bahn direct from the airport, and as noted above the S-Bahn runs from there to multiple other useful locations. The U-Bahn at Alexanderplatz is almost equally convenient. I liked the transit system because it has no turnstiles, you just walk into the station, up or downstairs (or escalator) if necessary, and onto your train. Much faster than the systems with turnstiles where people line up at busy times.

As in most cities, there are some unsightly or rough parts. You can Google to find out where they are. I suggest you avoid them to make your trip more memorable.

Let me be the third person to recommend the Adina Hotel at Hackescher Markt. I was there in October and it was convenient to everything.

Much is walkable from the hotel or just a few minutes by tram or U-bahn.

You can get a nice discount if you book direct. I booked a basic studio but because I booked direct they upgraded me to a one bedroom.

My favorite place to stay in the world is mittendrin boutique hotel. The owner/hostess is a former Munich stage actress whom I adore. Four rooms in a flat in an old Berlin building that was built around 1915 as I recall. Two bedrooms have their own bath; two bedrooms share a bathroom. It is located in the former West Berlin near Kaiser Wilhelm Memorial Church. Great public transportation connections. No air conditioning! Which may impact your decision depending on how late in the spring you are visiting. Amazing breakfast. I've spent 54 nights there since 2016.

https://www.boutique-hotel-berlin.de/

I agree with the others about Hackescher Markt being a great area to stay - very convenient and comfortable, great area to wander around also. Good to know about German History Museum under renovation - that's one of my favorite museums and cafes. Plenty others to choose from depending on your interests! The Berlin Museum Pass has a list you can scroll through.
I'll also be staying in Berlin before heading to Gdańsk the day before Poland tour starts, to play it safe. Have fun planning!

Don't miss the Pergamum Museum in Berlin, it is special.

We did Auschwitz, it will curl your hair, we had nightmares for a while, but it was important to see it. I don't recommend taking young kids there.

For WWII sites, Normandy and Belgium have some great sites.

Kraków wasn't bombed in WWII and is great.