Near the Vagen there is the Valbergtarnet Tower built in 1852 as lookaround of the town. From its top you can see a great wiev over the vagen and the old town of Stavanger. Inside the tower there is hte Vektermuseet.
A wooden fire watch tower was built in 1658. The city guard was organized appr. 1700, there were two tower guards and four gards patrolling the streets. In 1833 a major fire destoyed 60 houses in the area Holmen; both tower guards had fallen asleep and did not ring the bells or fire the cannon to warn the citizens!
The existing tower replaced the wooden one in 1853, but some of the guards' duties were taken over by the police in 1859, others by the fire brigade in 1866. The city guard system continued until 1922, when the last guard retired. The tower is now used as a museum and a view point.
The linked web page is in norwegian, but there are a couple of pictures. The main page stavangerguiden.com does have quite a lot of information in english.
I have made a travelogue with pictures of the view from the top of the tower.
This tower was built as a lookout-tower for the city guards between 1850-1853. The museum at the top of the tower shows the history of the city guards.
From here there is a nice view of the harbour (V?gen).