Hi PetPal,
It really depends on your interests. I'm a self confessed history nut & for me Berlin is fascinating for that reason. Nowhere else in the world can you find a city that was literally divided in two & it's very evident looking at the architecture etc.
Apologies but Absolute walks is actually in Budapest ! The tour group I had in mind was
www.berlinwalks.de I went on 2 different tours with them :- Discover Berlin & the Nest of Spies. Their guides are excellent & give you a really indepth tour. I went on a bus tour also which I didn't find near as good but perhaps if the weather is bad, it might be a better choice.
If you're there for a week I believe San Soucis is a beautiful place to visit. I hadn't time unfortunately.
If you only visit one museum, make it the Pergamon. They have the old gates of Bablyon. It's a huge place !
If it's shopping or nightlife I'd be useless for suggestions, though I believe they've plenty of both. I went with a preconceived notion that the Germans were stuffy & unfriendly & I must say they couldn't have been more helpful, so I came home with much changed views.
If you feel like splurging out a bit, have a cup of coffee in the Hotel Adlon in front of the Brandenburg Gate. It's an experience of old world luxury !
Also go to the glass dome on the Reichstag if you get a chance - everytime I tried queues were very long - the views from up there are supposed to be great.
Whatever you decide to do I believe you'll have a wonderful time. It's a really vibrant city. I've been to Berlin a few times & there are still lots of things I haven't gotten to see yet, so you'll certainly fill in a week no problem.I was there in early December & the Christmas markets were just magical.