When they leave Henneth Annûn for Cirith Ungol (in the second section in Journey to the Crossroads), Faramir advises the hobbits:
If you take my counsel, you will not turn eastward yet. Go straight on, for thus you will have the cover of the woodlands for many miles.
In the evening of the next day they see “high dim tops and broken pinnacles of old towers forlorn and dark”, and Gollum says:
This is the road from the Tower of the Moon, down to the ruined city by the shores of the River. The ruined city, yes, very nasty place, full of enemies. We shouldn’t have take Men’s advice. Hobbits have come a long way out of the path. Must go east now, away up there. And we can’t use this road. Oh no! Cruel peoples come this way, down from the Tower.
On the map in The Return of the King there is only one road visible, close to the feet of the mountains.
Where would Gollum have preferred them to go, why, and would it have been better for them and/or him?