Where would you recommend for someone to stay mate as an away fan on a first visit to the city
Well since I'm native, I'm not that much into specific accommodation currently, as there are many new places opened in recent years.
Regarding location I would recommend staying on the right bank of Sava river in "old" Belgrade and probably somewhere near Slavija square/roundabout would give you walking access to the stadium (25-30 min walk) and also close to central pedestrian areas and parts with bars/pubs/restaurants.