Hotel Elegia is located in a quiet street, a few minutes walk away from luxury stores including Louis Vuitton. Your nearest train station is Savignyplatz.
The location is safe, and quiet, there are some restaurants, especially around Savignyplatz but these can sometimes be expensive.
The hotel itself is fine, and because the layout is within an apartment block, it feels like you are really 'living' in Berlin. I would pay the extra euros for a private bathroom and if possible request that your room is not the one next to the communal bathroom as you will hear people going in and out all the time. Your room may also have 4/5 beds in there, so this probably isn't the best option for a romantic weekend in Berlin.
Reception staff spoke English but note that reception is not 24 hours and if you need something out of hours your call will be transferred to someone who is probably housekeeping and whose English is not as great.
You should also read the reviews on the tripadvisor website.
This is a good, cheap option for a first time in Berlin, and I was satisfied with the hotel, although given the choice again I would have booked somewhere in a more lively area, eg near Oranienburger or Friedrichschain.
Getting to hotel from Berlin Tegel airport is fine. Use Berlin transport 'journey planner' to help you. Take the 109 bus from airport and then change at Jakob Kaiser Platz for the U7 to Adenaur Platz and walk from there.