As a local resident i can give you a lot of recommendations.
while you are at the "Brandenburg Gate" area there are a few things to see,
Interesting buildings are Berliner Dom (have a look inside if possible) or Hotel Adlon.
Visit the holocaust memorial. Have a walk on the Friedrichstr. Maybe you would like to walk to the "Checkpoint Charly"
Or take the "Französische Str." to Französischer Dom and Gendarmenmarkt.
There you will find the "Deutsche Dom" lots of historical buildings and the Newton Bar
Interessted in shopping ? Nearby the Brandburg Gate you will find the "Mall of Berlin" one of Berlins biggest shopping areas. It is possible to take the doubledeck bus or a rikscha in this area.
Nice weather ? - This is a good chance to have a look at the historic berlin with a differnt viewing angle.
On Saturday i would take a boot tour at https://www.berlin.de/en/tourism/rivercruises-boattrips/3403158-3159294-river-cruise-historic-city-cruise.en.html
On Sunday i would go to mauerpark markt - bernauer str. you will find a lot of historic things there and of course open air music.- a different market location is berlin friedrichhain - boxhagener platz. Beware of pocket-pickers on both places.
Also interesting points are Flughafen Tempelhof - Take the tour, Olympiastadion - Glockenturm - have a look at the green side of berlin.
You want to see the nature of berlin? Visit the region "Grunewald" and "Wansee" If you are planing to go to Potsdam on the conference weekend there will be a wine fest at Werder it is nearby potsdam.
Wines are different from what you know. There will be wine from strawberrys , apples and so on. You can take a seat in a garden sit and relax and buy homemade cakes. There will be a fairground and a lot of nice places to eat roasted fish and taste the wine. How to get there ? Best is to take a boat at "wansee" you will cross the "Glienicker Brücke" - spy bridge.
You are searching somthing different - drop me a line.