What are the 5 must see places in Berlin?

That depends on what your interests are. You will get more insightful responses if you are a bit more specific.

For me they were the Reichstag, the Brandenburg Gate, the Gemaldegalerie (old masters), the Pergamon Museum and the Altes Museum (bust of Nefertiti).

You reading a guidebook

I'll have 3 days in Berlin in mid-Oct. It will be my first visit. Architecture, history, landscape and culinary are my interests.
Where is the city centre to be centrally located with access to most of everything?

3 days in Berlin is not a long time to see much on your list.
It is a very large city... locate in Mitte next to S and U Bahn
(Friedrichstraße and Unter den Linden intersection for example .

History.. probably more than you can handle.. but Berlin is in fact a pretty "young city".. not much going on there before 1800 or so... Brandenburg Gate, Reichstag, Jewish Museum, Allied Forces Museum in Dahlem, Potsdam (Sanssouci palace, no worries, a small palace, more like a manor plus the park)

Architecture.. the old/imperial one: Unter den Linden avenue is a prime example, Bauhaus museum, the fascist period (Tempelhof airport, for example), the socialist/stalinist period (Karl-Marx-Allee from Alexanderplatz to Strausberger Platz)

Landscape.. that's a tough one. Berlin is flat as a pancake. If you need a break from the city, go to Potsdam, visit the park and Sanssouci palace, or take a cruise on the Spree river.

Culinary.. i'm really not good at this one..