Euclidean shortcuts ignore one-way streets, staircases, detours, and weekend crowds. The best engines pull travel times from transit schedules and road graphs, then compare routes by minutes and comfort. Sometimes the seemingly longer path wins because it avoids bottlenecks and offers better scenery, giving your day more joy per step.
Greedy starts are fine if refinement follows. Local search moves like 2-opt untangle crossing paths, while time-window feasibility checks keep promised visits realistic. Multi-criteria scoring balances distance, ticket commitments, and personal priorities, preventing over-optimized, joyless sprints and nurturing itineraries that feel both smart and human, even under unpredictable city conditions.