JES, perhaps my opinion is clouded by the game I'm familiar with, but that's a heck of a lot of weapons for such a small ship. All the source material I've ever seen (two games, three different sets of blueprints, etc.), gives the Constitution-class cruiser four photons and three pairs of phasers on the saucer plus another pair on the secondary hull.
I would propose that this ship have two photons forward (but not in the bridge bubble ... I hate that idea as all the TV episodes have the photons coming from the under side of the saucer), twin phasers forward, singles phasers port/starboard, a single phaser aft, and twin point-defense 360-deg phasers on the ventral of the aft hull. A war-time upgrade would probably twin up the side and aft phasers and add another pair of 360 point-defense phasers on the dorsal.
I suppose that seems like a fair amount of armament for a Starfleet Destroyer, and the aft weapons and point defense phaser emplacements might even be left out when first launched (it seems the Constitution class lacks these in most schematics, suggesting to me that they are added during upgrades, in order to amend firing arc blind spots) but I also think that would be the minimum by 2260.
It can be hard to tell though, since different sources suggest different weapons mountings for ships of that era.