The Ubahn line 2 runs by the Opera House as well as Bahnhof Zoo and Wittenberg Platz, the commercial centre in the former west Berlin. YouŽll be spoiled for hotel choices of all comfort levels in that area. And a 3 star hotel at the price range you name shouldnŽt be a problem at all. But read up on them on Tripadvisor, Expedia etc and look out for bargains.
But IŽve allways found www.hrs.de mentioned earlier in this thread the trusted ally when IŽm booking hotels in Germany.