There are four habituated gorilla groups in the Virungas, and it really is the luck of the day which group your permit is assigned to.
The Sabinyo Group and Group 13 are both within reasonably easy walking distance, whereas the Susa Group can be up to 4-5 hours walk away. (This is the original group that Dian Fossey studied) The Amahora Group is marginally nearer than the Susa Group.
Be prepared for a steep scramble!
Well that's a one day track you could to if you are in top shape and acclimatized to the altitude. It's about 10 -12 hours climbing to the Muhabura pick at 4100m, and the air is very thin there. Seriously i believe this is better done in two days but such option does not exist. Don't dream of doing it on the first day you arrive.