In the end, they still stayed at the hotel because the hotel's conditions were indeed much better than the headquarters of the Warfire Group.
Warfire Group's headquarters in Baghdad was a combination of office and dormitory, and the conditions were not too bad, but certainly not too good either. Dawson had rented a nice house for himself in Baghdad, but he couldn't possibly invite Gao Guang to stay at his place.
Salah didn't go to the hotel with Gao Guang because Salah still needed to keep his distance from Moussa, so to outsiders, it looked like Salah had just visited his nephew, but ultimately, due to different philosophies, he left after just a glance.
So Dawson and Sanchi talked for a full two hours in the hotel where Gao Guang and the others were staying, and no one knew what they discussed, but Sanchi indeed seemed pretty happy when he left, which suggested he had gained quite a bit from Dawson.