I don't know what the hotel Melia is charging these days, but it is an excellent hotel with an excellent location for sightseeing in eastern Berlin, with great transportion links to the entire city. There are many hotels of high quality in eastern Berlin, not only to serve the tourist trade but also the many people who come to the city to do business with the seat of government (which is located in eastern Berlin).
Reading recent guest reviews on booking.com and tripadvisor.com should give you a good idea of what's attractive to you in your price range.
Also bear in mind that if the Wall is your focus, that the wall divided the city into east and west sectors, so you can be staying near where the wall was whether you stay in west or the east.
Berlin is generally a much safer city than any city in America, and might even be safer than London and Paris or Amsterdam. When I stayed in eastern Berlin, the only time I worried about my safety was when I spotted a coyote trotting along the banks of the Spree late at night. There are no doubt isolated parts of the city where tourists are advised not to wander at night, and rough bars you shouldn't be drinking in after midnight, in both the eastern and western areas of Berlin. But again, travelers who write hotel reviews are usually very quick to say if they felt unsafe where their hotel was located.
Here is an overview about safety in the city from a website that advises people about renting apartments in Berlin (the whole website provides a good overview of Berlin):
Safety, especially for Women
Berlin is still extremely safe, day and night, especially inside the circle S-bahn line. But it should be mentioned that, as a precaution, visible minorities might avoid some of the Eastern neighbourhoods outside that S-Bahn line: Hellersdorf, Marzahn, Lichtenberg. They have a reputation for being right-wing and have almost no ethnic diversity. The same goes for parts of the surrounding region of Brandenburg. While most women find Berlin extremely safe, day and night, some have been verbally harassed in outlying areas of Neukölln walking home alone at night. Riding a bike helps matters. Neighbourhoods like Mitte, Prenzlauer Berg, Schöneberg and Kreuzberg are generally worry free for women who feel like targets of unwanted male attention.