Which particular area around Berlin is the most convenient for sight seeing when searching for a hotel?

City centre hotels are good and less expensive than their equivalents in Paris or London. Try the Dorint or the Tiergarten for starters. They're north of the main drags but have easy access to everywhere.
Lots in and around the Ku'damm at all sorts of prices.

If you are new to Berlin then for sightseeing use the Zoo as your Centre of Operations. This area is a good S and U Bahn hub and is also the main bus station.
It's easy walking to Ku'damm, Europa Centre and major shops.
Take the bus route 100 (from the Zoo) for a tour of other main sights inlcuding the Brandenberg Gate, Teirgarten, Reichstag, Museum Island and Alexanderplatz.
Look at the BVG.de web site for transport information.

Enjoy.

You could try Potsdam. It has a splendid castles and parks, is not so crowded as Berlin and you can still be in Berlin center within less than an hour.

Try charlottenburg its just off the motorway has easy access to the town centre and has plenty of hotels

depends on "what berlin" you want to see.
my choice would be "Mitte", around "Museumsinsel" (Museum Island) and friedrichstrasse-station: there are a lot of small hotels (around 'hackescher markt') and some big one also (on famous friedrichstrasse / unter den linden or even the "dom aquaree" near 'alexanderplatz' ) ... a lot of choices. and the best: you can WALK to the most famous points in berlin (brandenburg gate, friedrichstr, museum, alexander plaza), have nice day-trips and enjoy the night-life also, if you want so.

Assuming you do not have a car, there are two good places. One is the area near Bahnhof Zoo. That's very central to the former west, and sights in that area.

But the real best place to be in in Mitte, in the area of Unter den Linden, Parisier Platz, Alexanderplatz and Museumsinsel.