Hola Colin

The sentence "No puedo salir hoy pero saldré mañana" uses "pero" instead of "sino" because "pero" introduces an alternative or additional idea, whereas "sino" is used to negate the first clause and replace it with the second. In this case, "pero" connects two independent clauses where the second does not negate the first but provides additional information.

"Pero" is appropriate here as it contrasts two different circumstances without the sense of replacement or correction that "sino" conveys.

Saludos

Silvia