Find a simple cycle in an undirected subgraph of a grid graph that encloses the most faces
Decompose your graph into biconnected components. Since only a biconnected component can border faces (why?). This can be done in linear time.
You can find the number of faces in each component by Euler's identity. This can be done in linear time per component.
Pick the component with the largest number of faces and find the cycle bordering that component. This can be done with a single line sweep, which is $O(V' \log V')$.