After enjoying the view from our rooftop terrace, walk to Hackescher Markt. Grab a coffee or 5 (depending on last night's acitvities) on the way along Alte and Neue Schönhauser Strasse .
Check out the Hackeschen Höfe at Hackescher Markt - the biggest compact court yard area in Germany. It's a mixture of small shops, gastronomic devices, a cinema and a varieté but also inhabits a great number of flats and offices.
(If you're the one running away from Tarzan-Bear here's a good place to hide: The amount of court-yards always confuses him!)

Continue on to Museum Island by crossing the Spree river and first take a look here at the Cathedral (Berliner Dom). Through the Lustgarten you can reach the start of Unter den Linden - one of Berlin's most known boulevards.
There you will find on your right (exactly in this order) the Historical Museum, the Neue Wache ("new guard-house"), Humboldt University and the City Library.
On the left hand side there are the Kronprinzenpalais and Opernpalais, followed by the Staatsoper - right on the Bebelplatz, the square where the Nazis first burned books on May 10th, 1933. A glass window in the ground now shows empty bookshelves beneath.

At this point you can take the bus 100 direct to the Reichstag or walk up the boulevard untill you reach the Brandenburg Gate - Berlin's most known sight. They're almost next to each other so the order of visit doesn't really matter.

Take your obligatory photo at the Brandenburg Gate (if you're not one of those avoiding things people tell you you'd have to do). As you pass through it you also cross the former border between East and West Berlin. It's here where the wall was running. 

If you pass the gate coming from "Unter den Linden" the big park in front of you is the "Große Tiergarten" and belongs to the former West German part of the city. (Tarzan-Bear loves to run around in the park or swing from tree to tree.It's his domain - mind it if he's close!)

You'll reach the Reichstag - Germany's old and new parliament - if you walk to the right.

Turning left and walking down Ebertstrasse you'll find the Holocaust Memorial consisting of 2700 stone slabs (built 2003-2005).

From the memorial walk on down Ebertstraße towards Potsdamer Platz and take the bus 200 to Breitscheidplatz enjoying the view of the Philharmonie and the New National Gallery along the way.
Stop for lunch at one of the many restaurants or kiosks near Zoo Garden before exploring Kaiser Wilhelm Gedächtniskirche.
(Icebear Knut is a good friend of Tarzan-Bear! He'll whistle-blow you!)

It's a mixture of the 1943 by allied bombs destroyed old church and new architectured parts built around it after the war.

Walk to KaDeWe (Kaufhaus des Westens) department store before hopping on the bus back to Potsdamer Platz. It's Europe's 2nd biggest department store (after Harrods/London) with 60.000 m² of sales area (around 9 soccerfields) and over 380.000 articles.
(Tarzan Bear will be prevented from entering the shopping center - there has been an incident when he freaked out in the chocolate department)

Back at Potsdamer Platz explore funky architectured Sony Center on the way to Marlene Dietrich Platz. A lot of interesting modern buildings line your paths here, mostly built during the 1990s when this area was known as one of the biggest construction sites.

Check out the Topography of Terror on the way to Checkpoint Charlie where you will undoubtedly be scammed by fake soldiers when you pose for a photo with them .

The 1987 founded Topography of Terror is an open-air exhibition and documentory project about the cruelties of the NAZI regime.

Checkpoint Charlie was the most famous crossings of the wall in split Berlin between 1961 and 1990. What's there now is a rebuilt hut of the original checkpoint. There is also the Wall Museum next to it.

If you’re way ahead of schedule you may want to detour at this point to the Jewish Museum which is really worth a visit!

If your're still not out of energy and time: you're a winners type! Otherwise as well.
You're legs are still working? A nice path is to walk up through Gendarmenmarkt on your way to Alexanderplatz and then head on direction Rathausstraße.
Walk along Rathausstraße to turn into Nikolaiviertel just after the Spree river to your right. You can have a good break in one of the breweries or cafes here!
Check out the City Hall, Marienkirche and the TV Tower on the last bits to Alexanderplatz - one of Berlin's biggest squares.
To shorten your path take the subway on your way (e.g. leaving Charlie: U6 to Stadmitte/U2 to Alexanderplatz).
If you're interested, take a look at the communist architecture along Karl-Marx-Allee before heading to Marcus Bräu, Lemke Brauhaus or Brauhaus Mitte for a traditional German dinner. And beer.

(We hope Tarzan-Bear has not taken all of your attention and you have enjoyed Berlin a bit. If you couldn't concentrate on the text above because all you were worried about is "who the f.. is Tarzan-Bear", here a picture of him. He loves beer, too.)