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This question got me thinking about launch site selection for missions to Mars. I assumed the optimal launch site inclination would be the one where Mars is due East. Depending on where Mars is in its orbit, this would be at 23.4° ± 0-1.85° (Mars's orbit has an angle of 1.85° wrt the ecliptic). Or would you be better off launching from the equator at an angle of 23.4° ± 0-1.85°?
Or is the solution different altogether?
I would say, anywhere where the line of the ecliptic is directly overhead. In other words, anywhere between the line of the Tropics (with two launch windows per day), so your suggestion of near the equator is good.
Though it has to be said that as Earth's velocity along the ecliptic is already pretty high, launching from outside the optimal tropical area is a relatively small penalty...
In fact there is no penalty for launching an interplanetary vehicle from a higher latitude, apart from the rotation velocity benefit. Even in a polar orbit, it is easy to achieve an escape trajectory parallel to the ecliptic, or if you prefer, at ± 1.85°:
Of course, the launch window for that only appears two times a day.
