1. Did you factor in that your home is a heavily leveraged investment? Yes you are paying more interest in the city, but you also have a more valuable asset; an asset that appreciates. You get to keep the appreciation and can pay the bank interest in inflated dollars.
2. Did you calculate the cost of owning a car (maintenance, insurance, speeding tickets, registration, gas)? because not needing to own a car (or cars) in the city helps to offset some of the increased living expense.
3. What about the cost of commuting, both in time and money?
Do the math. People in cities pay more to live in a smaller location--but 20 years down the road they typically have a higher net worth because the increased expense is towards an appreciating asset, rather than spent on consumables (gas) or depreciating assets (cars, jet skis, motorcycles, and [in some cases] over-built houses for the area). People who live in cities are also healthier (due to more walking and less time sitting in traffic).