Since you're on the second-best aluminum hardtail Specialized makes, and it's probably indistinguishable from the Stumpjumper HT if you were to strip the paint off of both of them, it would totally make sense, at least to me, to keep this thing for the rest of its life and keep upgrading as needed/desired. Assuming that a 26" aluminum hardtail with a 80-120mm fork is your platform of choice.
For me, contact points, between you and the bike and between the bike and the ground, are the first priorities. So +1 for good tires.
Having good bike fit is the single biggest upgrade you can ever make. Experiment with your spacer stack and stem position and think about a different stem and handlebar. If you're not happy with your saddle, get a new one. If your seatpost doesn't let you put your saddle in the right place, get a new one. I like bar ends a lot, so that's something else to consider. People might make fun of you, but whatever - if it's a riding position that's useful to you, there's really only one person you need to please.
I've got a nice fork on my Hardrock that I got on EBay. So you might also start watching EBay for things to show up.
Better front derailleur. Shimano Altus is pretty flexy. Going to an SLX on mine was a big improvement. SRAM shifters are supposed to be compatible with Shimano mountain FDs, but you might want to brand-match just for the sake of consistency. Or not.
Better crank. Mine's the same as yours, and the tread's too wide, which hurts my knees. It'll be replaced with an SLX when I'm less broke. You might also experiment with a different length crankset. At your height, you may be happier on something with longer arms.
You might consider going to nine-speed at some point. It will require new shifter pods and a new cassette and chain. It depends how sensitive to cadence you are. Hopefully, nine-speed components are about to get a lot cheaper, since SRAM's releasing their XX group.
Nicer wheels, maybe. If yours are the same rims as mine (looks like they are) and you're more of a cross-country guy, you'll probably be happier on lighter, narrower rims. Check the width - it's on a sticker on the rim. It's probably a 22mm rim? That's a quite a lot, and a 2.1" tire can sit a little oddly on something that big, in my experience.
My teammates highly recommend Shimano XT disc brakes. The BB5 will eat an entire pad set in an hour and a half if you're racing and it's muddy. Terrifying when it happens. If you only ride in nicer or moderately damp weather, you'll probably get over a year out of a set of brake pads, though.
Bikesnob has a joke about how eventually people feel the components are too good for the frame, get a new frame, and now have two bikes basically for the price of three. So try not to let the upgrade fever hit you too hard - try to limit yourself to tires and fit issues, and then replace things only as they break or wear out. Aside from the front derailleur, your bike's got a really solid spec.