This problem seems to be a variant of the Traveling Salesman Problem (TSP), which is known to be NP-hard. This means there's no efficient solution for large datasets, and brute force methods become impractical. However, there are several heuristic approaches that can provide near-optimal solutions in reasonable time for practical instances of TSP. 

1. We need to consider the cities as nodes in a graph where edges represent the travel costs (like distance or time) between pairs of cities.
2. Given the goal is finding the "fastest" route, we'll likely use time as our primary metric rather than physical distance.
3. Common heuristics for TSP include nearest neighbor, minimum spanning tree methods (like Christofides' algorithm), and more sophisticated ones like genetic algorithms or simulated annealing. 
4. The optimal approach might depend on the exact details of the problem - number of cities, their distribution, and possibly constraints like one-way streets, etc. 

Given these considerations, a practical approach could involve using optimization libraries that implement TSP solutions with customizable heuristics.