We prefer to stay in upscale apartments over hotels. Generally in the center, close to historical attractions and good restaurants, in areas that are safe and pleasant to walk. We like the space of apartments and usually look for ones with terraces or balconies to enjoy a quiet evening after a long day of sightseeing.
Going to Berlin in a few weeks, very limited supply of high end apartments. We found 2 interesting places, one in Kreuzberg, one in Kurf�rstendamm .

We understand the areas are very different. Kurf�rstendamm seems to be famous for upscale shopping (we are not shoppers), while Kreuzberg is very hip and trendy (we are neither).

But if we want to be near the historical sites, both seem to be rather far.

Our third choice is the Intercontinental in Mitte, which has everything, except it's a hotel, and we prefer apartments. But it's actually free (on points), so it's really hard to say no to free.

Is Mitte much more suitable for our interests than either K'damm or Kreuzberg?

I say yes, but Intercontinental is quite near to the K'damm (OK, it's a long street with different areas). For historic location best would be something near "Unter den Linden", Gendarmenmarkt or even Alexanderplatz (not a nice area if you ask me). Potsdamer Platz is also good.

Take the Kudamm area, its nice and you will be in the sightseeing areas using public transport in a few minutes.