I'm sure there have been threads about this before.
My wife picked up a State Bicycle fixie/single speed for me over the holidays. I tested out the bike on one of the days that we had some nice weather. It has the bullhorn bars and I'm not sure if I dig them now that they are just a bit to low for me.
I've been looking at riser bars and at stem risers.
Just get a stem with more rise to it so that the bars sit higher.
The stem riser will change the feel of the bike when going "no-handed".
I would describe it as a "squirrely". IMHO, not the best customization.
As suggested, change out the stem.
If it is close you might be able to flip the stem and get almost a half-inch or so more rise with what you have now and not need to buy anything. It looks like most of the State Bicycles come with 87/97 degree stem and usually ship in the lower position.
Or if that isn't enough change for you then just get a different stem. There are a ton of options in a larger angle and shorter length for raising the stem and pulling it in from what you have now.
For around $20 you can get a lot more elevation with something like this. You will have to mess with your headset a bit and need to re-tension your bearings, and properly torque the pinch bolts on both the steer tube and the handlebar when you flip or swap stems. If you have carbon fiber bars and/or fork w/ steer tube you will want to pay close attention to the torque values and get a stem that is for CF (which will cost more most probably.)
Sheldon tells you about how to adjust threadless headsets here or you can just take your bike to our LBS for the work and ordering parts.