That is the perfect place to have a hole. But don't patch it, get a patch/plug. First off, though, I would suggest finding someone who repairs tires professionally. If that is not an option then read on.
You want to first find a patch-plug kit. These usually have two plugs and cost under $5. It looks like a circular patch with a plug attached to it. Now the patch part itself should have a soft rubber compound on it, if not, don't buy. Once you have bought the kit, go home and dismount the tire. Make sure you mark the tire where valve stem is so you re-mount it at the same location. That makes re-balancing a bit easier, or you can just re-mount it with the patch opposite from the plug.
Once the tire is removed from the rim, find the hole. Drill or ream the hole. If the nail went in at an angle, drill straight through the tire from where the hole is on the INSIDE of the tire. Do not attempt to drill it in the same angle as the hole, it must be normal (as opposed to tangent) to the surface.
Now the tricky part. A Dremel with a sanding attachment comes in handy here. See the inside of the tire? It's ridged and textured. It is also made of a high-silicone content rubber. A full tube of rubber cement won't make that patch stick as it is. You need to CAREFULLY sand the inside surface where the patch will contact smooth. You can't take too much as it will compromise the structure. You can't take too little or else it won't stick.
Once it is smooth on the inside and the hole is properly reamed, get some cleaner, like alcohol, and clean the inside surface. Vacuum the inside of the tire to remove any loose rubber and debris. Not doing this will affect the balance later on. Apply the cement to the tire and the patch and let it sit for a moment to slightly dry first. Then press it on and roll it from the center outwards. Keep pressure on it for a few minutes and then check the patch. You should be ready to remount and rebalance now.
SO, with all that said, a lot of people who have never repaired one will just tell you to buy a new tire. That's fine, too, it's your money, and if you do high speed sustained runs, this is probably wise (repair knocks off one speed rating).
Myself, I have just changed my last tire which had been running with a repair for over 2K miles. I got a punctured tire from another member to replace that one and have been running it almost 1K miles already.
And with that said, if you choose to replace rather than repair, I would be willing to take that tire from you instead of seeing get thrown away. Let me know.
Thanks for all the great opinions! I was looking for someone who had a repaired tire go bad but seems no one has. I took it off the rim this morning and the local tire chain (Discount Tire) Fixed it for free. They let me watch them repair it and guess what Narc, They did exactly what your first post said to do. They didnt even give me any crap like I was expecting, just good professional service. I feel confident to run her the rest of the year. Probably buy a new one over the winter. 
