Balzaphon, like Scorn, is a lich. Like Scorn (and most liches... lichen?), he's primarily a Frost-based caster. You can find him within the burning streets of Stratholme, and while you can get at him by going in the front door, it's much easier to use the eastern entrance that takes you straight to the Undead side of Stratholme. You need the Key to the City to get in through that way, so if you don't have it, bring someone with one! Or fight your way to this spot through the other entrance.
If you go in through the Undead side (as you should) then you'll see a fork in the road just inside. There's an open gate on the left, and a locked gate up ahead. You want to hang that left, where you'll see a fountain surrounded by undead. Clear a path to the right, watch for abomination patrols, and hang that right. You'll see Balzaphon right up ahead. Before you fight him, clear around him. He has a Fear, so you should be careful in this area.
Ready? Fight! He rapid-fires Frostbolts. And I mean rapid. He casts them very quickly, and he casts them one after the other. If he takes a break from that, he casts AOEs (Frostbolt Volley, Cone of Cold) instead. Your tank will need a whole lot of healin' here. When his health starts dropping, he'll start mixing Fears in there on people, which is why you cleared around him. It's very easy to get feared into nearby groups of undead.
It's a harder fight than the earlier bosses, but Lord Blackwood is a little more tricky, I think. You'll get Balzaphon down pretty easy, just stay alive longer than he does! Easy! Right?
Now, the loot. Again, Balzaphon is caster heavy. Sort of what you'd expect from a lich. He has a spell power necklace, Chains of the Lich. He has a spell power belt, the Waistband of Balzaphon, that is marked as being frost spell power only on Wowhead but I was under the impression they has removed all class-specific spell damage/power, so who knows! He also forks over his staff, Staff of Balzaphon, from time to time.
Back in the day, the biggest draw about this guy is that if you're after Argent Dawn reputation, he drops two Corruptor's Scourgestones and he's only a handful of pulls away from the entrance. You could farm up a dozen of the things in no time flat. If you're looking to complete the Argent Champion achievement and need a lot of Dawn rep still, this is a good place to go.
If you want other bonuses, if you go a bit further up the road from Balzaphon you'll come across The Unforgiven. It's only a few pulls away, so it's some extra loot and scourgestones. And if you want to go a little further than that you'll find Hearthsinger Forresten, who will sometimes drop the Piccolo of the Flaming Fire, a trinket that will annoy your friends for eternity.
That's it for the level 60 bosses from the Scourge Invasion! The only one left now is Tenris Mirkblood inside of Karazhan. Good luck!