Oh, there is so much to see in Berlin, it is really difficult where to start.
I think wether you want to take a tour or not rather depends on which kind of experience you want: try to see as many things as possible or just experience some highlights, but have more time for them...
A lot of the main sights are walkable, but keep in mind that Berlin was divided for quite some time and therefore has not one main city center, but rather two (also it grew together from two towns).
Most of the main sights however are very close together, the ones that are further away are the Kaiser-Wilhem-Gedächtniskirche, the KaDeWe (Kaufhaus des Westens, the largest department store) and Charlottenburg.
But one can make quite a nice walking tour from the main station (Hauptbahnhof) over a pedastrian walkway to the parliament building (Reichstag) while passing also the chancellor's residence (Bundeskanzleramt) on to the Brandenburger Tor. From there follow the Ebertstraße past the Holocaust memorial to the Potsdamer Platz (the Berlin Wall was standing in the middle of this street), then turn left into the Leipziger Straße where you will pass the former Prussian parliament (which houses today the Federal Assembly). The turn right into the Mauerstraße and follow this to the Friedrichstraße where you have to turn right and walk one block down to Checkpoint Charlie. The turn back on the Friedrichstraße and walk this towards the north (you will then cross again into . Turn right into the Mohrenstraße towards the Gendarmenmarkt (and wave to me when you are there, this is where my office is

). Have a look at the Fassbender and Rausch chocolate shop at the south-west corner of the Gendarmenmarkt. Then turn left onto the Gendarmenmarkt and just cross the square. Continue north on the Markgrafenstraße and then turn right into the Behrenstraße which will lead you to the Bebelplatz. In the middle of that square is a memorial for when the Nazis burned books by authors they did not approve of. You have to look for it, is on the ground: a basement of empty shelves. Then walk Unter den Linden towards the east: you will pass the Opera house, the Humboldt university, the Neue Wache, the German Historical Museum (and many more buildings) and then the Museumsinsel (museum island) and the Deutscher Dom (German cathedral). If you want and have the time, continue to the Alexanderplatz to the TV tower. You can take an elevator to the top and on clear days you will have a wonderful view of Berlin. There is generally a line, but it moves quite well.
Then hop on a bus with the number 100 or 200 and get off at the stop Unter den Linden/Friedrichstr. (or walk Unter den Linden all the way back towards the west), walk a bit further west towards the Brandenburger Tor and have a look at the Pariser Platz (including the US Embassy). Then either walk through the Brandenburger Tor and back to the Hauptbahnhof to get on your train or get into the underground (U-Bahn) U55 to travel to the main station. If you buy a single ticket on the bus it will be valid for the U-Bahn as well.
This is quite a lot of walking. I tried to measure it with google and it seems that one way would be about 3.5 miles to the museum island.
End of July can be really hot, but also cool and rainy. I think anything between 60 and 90°F is possible, most likely somewhere around mid 70s. However, keep in mind that we don't have as much air conditioning here. So most restaurants won't be good places to cool off inside.
Two places which might be nice for lunch along the route outlined above are: Schinkelklause (Unter den Linden 5, east of the Opera House) or Augustiner am Gendarmenmarkt (
http://www.augustiner-braeu-berlin.de/), which is Bavarian, so not really that authentic. But my sister tried it and said that it was pretty much the real Bavarian thing (we grew up in Bavaria). The Schinkelklause is more real Berlin food. Oh, and next to the Schinkelklause there is also a very nice cafe with cakes!
And of course if there are any more questions, just ask away!