When you hike up the Doi Suthep mountain, you actually don't get the view of the town until you reach certain viewpoints. Most other times along the path you would only see the jungle.
There are a couple:
Viewpoint 1: Doi Suthep Temple
There is a path around the main temple which leads to a large lookout terrace with excellent view over Chiang Mai. However it tends to be very crowded during the day unless you go super early or close to sunset
Viewpoint 2: On the way up to Doi Suthep Temple
Just before you arrive at the temple, you will see a small lookout platform that also has amazing views, very peaceful and less tourists