The point of the battle bridge wasn't to have a 'safe' bridge, but to operate as the bridge for the rest of the ship once the saucer section had seperated and flown off.

Well, I guess there is that. But then couldn't have been better lit then?

Well, then we wouldn't have known just how serious the situation was. I mean the only way we know the Klingons are the bad guys is because you stumble through their ships in dimly-lit red light and fog.

Or why all of Voyagers lights turned off, when they went to Red Alert

I think it was so they could see the buttons. Bright lights and shiny glass can make the difference between firing torpedos and ordering a pizza

As was indicated by other posters, it is very much atop the stardrive. It did however look better armored than the regular bridge, being submerged at least partially into the deck, ala a Defiant-class bridge.

However, when interconnected, the battle bridge still has a few decks worth of cushioning and a second layer of hull between it and attacks. As such, the battle bridge being used in combat offers the best of both worlds - instant ability to separate and fight (never mind the all-important question of what to do with the saucer - doubt the Romulans or the Borg are going to patiently wait for you to fly off 5 minutes' warp away, ditch the saucer, and then come back), but also extra protection for the active command center in separated flight mode.

That said it wouldn't surprise me if the battle bridge had a skeleton staff on at most times, or at least at yellow alert, just in case something happened to the main bridge.

Aside from Enterprise, before shields were invented, Trek technology has generally portrayed the hull as having the resistance of wet paper when hit with full power weaponry. Undiscovered Country showed a good example, because one single torpedo went through the entirety of the saucer with no signs of being slowed down once the Enterprise's shields went down. Therefore, it really doesn't matter where you put the bridge, because once the shields go down you're equally vulnerable regardless of where exactly the bridge is.