Make sure you have unlocked Rex Fury before attempting this. You get his character token on the last level of the game. I actually had to visit 11 stone statues for my achievement to pop. This is the order I did it in. All you have to do is walk up/drive up near each statue. Nothing else. You can also save yourself some time and go after the Skullputre Vulture achievement while traveling around the map. (Destroy the 5-hidden Rex Graffiti Skullputres.)
1). Cherry Tree Hills: Mailman Statue- Is on top of awning of a building next to billboard of a baseball player. Head north towards Auburn and it will be on the right side of the road just before entering Auburn.
2). Festival Square: Baseball Player- located in the very south of his area before entering Downtown.
3). Downtown: The Artist- In front of the odd shaped circle with two dots in it on the map. I think this is the visitor center. Bottom/south end of downtown.
4). Downtown/Lady Liberty Island- Lady Liberty Statue: The entrance to the Island is located in Downtown just south of the Artist Statue. Located in the middle of the odd shaped circle with to dots on the map. You need Rex Fury to open the orange box and then teleport with the astronaut to the island.
5). Kings Court- 4 Soldiers Statues- These are located around Blackwell tower. Make sure you drive/stop by all 4. The tower is located in the west of this area.
6). Fresco: Soccer Player- It is north of the leaning tower just before entering Paradise sands.
7). Lego City Airport: Saluting Pilot- Look for the circle road on the map. The freeway crosses over it. The statue is located near that circle.
8). Bright Light Plaza: Gladiator lifting a Globe- It is in the middle of the circle on the map of area. You can actually jump a car threw it.