I'll start with the hostel itself which is extremely clean, the beds are comfortable, and you have all the facilities you need such as free internet, washing machine, 24 hour check in and staff, nice showers and bathrooms, various sized rooms ranging from 8 to private, free tea (great selection! :) and coffee etc... The price for what you get is very cheap, and if you book online even cheaper! Great atmosphere too, courteous people, you will be able to sleep if you are tired, but on the other hand you can meet people to go out with even though the hostel is not huge. I stayed there for less than 2 weeks but I met Serbs, Germans, Australians, Irish etc
The hostel location is perfect. If you are traveling to or from the airport, the shuttle departs and leaves from just outside the hostel, at Trg Slavija. If you are coming from the train station, that is just a few minutes walk down the street. From the hostel you can walk to the main street Knez Mihajlova, Kalemegdan, the bohemian quarter and other tourist attractions such as the rivers....if you walk in the other direction you can see saint Sava's temple (really amazing at night), and Red star and Partizan football grounds. So basically Trg Slavija (where the hostel is situated) is really a great central location, lots or trams, buses and trolleybuses stop and depart from there.
The best thing about this hostel however, is the staff. Tina and Ivan who run it are extremely helpful and friendly, Great English (and also French) speakers. They welcomed me with traditional wine, and were able to recommend the best places to go out to on a night and visit during the day, they also know about all the practical things like cheapest transport, exchange offices etc. They very quickly found an apartment for me which was great because I needed longer term accommodation to work. They would definitely help with any problem or question that you have.
I would really recommend staying here, it's great for all criteria! Thanks guys!