The practical framework
Transportation costs include fuel, maintenance, insurance, parking, tolls, transit passes, rideshare, and time. In some places you can drop a car. In others you may need a second one. That single change can outweigh a rent difference.
Run the commute in normal traffic, not just on a map at midnight. Time has economic value. A longer commute can also affect childcare pickup, exercise, meal planning, and stress.
Insurance can change dramatically by state, ZIP code, vehicle, and coverage. Before moving, price your actual car and driving profile in the target area.
What to do next
Run your numbers through the tools, then replace assumptions with quotes. The goal is not to predict every dollar perfectly; it is to find the expensive surprises before they become commitments.