What are the long term consequences of building with your second settler?

Think about the shield production of your first city and irrigation/roads it needs. Can you build a third settler in the time your settler is upgrading? Churn out settlers from that city, rely on new cities for production, and use the foodless settler for roads.

Is there a danger/need of early armies? Make that settler into a city quickly, unless it will stretch your potential defenses (2 cities shouldn't), in which case consider joining it into your first city after a few improvements.

Does your first city lack the ability to churn out new settlers, no matter the improvements that can be made (not uncommon)? You're going to want that second city with the ability to increase your production. Limiting yourself early on can put you dangerously behind.

If you've got time, try an iterative experiment. Compare the state of your civ 50 turns in with the second city built and without on many maps.