I decided to follow Sindig after leaving the Grotto to see what he was up to. He walked (very, very slowly) to Honningbrew Meadery and then turned south to Riverwood. On the way we passed a few Whiterun guards and an Imperial prisoner convoy all of whom ignored Sindig. As we travelled south to Riverwood we met up with another Werewolf heading north. This Werewolf was also named Sindig. I was rather conflicted as to which one to follow, but decided to stick with the original Sindig. He then proceded to Riverwood (9 AM) and took the road to the east heading up the mountain. Again, no problem with the town folk or the guards. At that point I ran out of patience. Who knew if he would ever stop? So I stopped following him.
But I am sure someone must have followed him further than I did and can report back where he goes.