There aren't really any "safe" places in a starship's hull if the heart of the saucer doesn't count as one. So one's placement of such a facility would depend on things like
- what one wants to achieve with it (immediate taking over of all main bridge functions if said primary location takes a deadly hit, or a way to operate auxiliary systems when most of the ship has been wrecked?),
- how one intends to crew it (top staff rushing off the main bridge to assume new, "fallback" positions, or a "shadow" team sitting and waiting for the main heroes to die so that they can start collecting their own pay?), and
- what is supposed to happen later, after successful transfer of control from main to auxiliary (the skipper moves his favorite coffee mug to the auxiliary bridge for the remaining three years of the mission, or everybody retreats in a controlled manner to the escape pods and shuttles?).
In TOS, the existence of a "shadow command crew" seems to be ruled out. Auxiliary control is generally deserted, and for that reason easily taken over by hostile forces.
In TNG, the main heroes move from main to battle bridge as needed, and have a rapid means of doing so. In TOS, the assumption probably would be that Kirk would never "preemptively" retreat to auxiliary bridge, but would die on the main one with his boots on, so there's no need for an express turbolift or somesuch. When needed, people would be rushing to the auxiliary facility - but from places other than the main bridge, because anybody rushing from that direction would probably succumb to the thing that took the main bridge anyway.
TOS also features the "emergency manual monitor" facility adjacent to engineering, apparently a facility for controlling just the essential engineering functions if main bridge kicks the bucket, and distinct from the place that would allow continuing overall control of a battle or other mission on such an occasion. Auxiliary control thus sort of bootstraps itself into great significance and a true "second bridge" identity - something the many hostile takeover plots also seem to rely on.
It would thus seem that the TOS auxiliary control center need not be quickly accessible from the main bridge; need not be placed particularly close to last-ditch functions and resources (since the EMM takes care of those); doesn't see much "peacetime" use; and might indeed be something that usually just keeps on gathering dust but is a vital spare on long missions, only fired up in the aftermath of a crisis rather than during one...
The center of the saucer sounds fine to me for placing such a spare. The less it differs from the main one in all respects, including placement, the better.