Id keep the spare.
Its going to be a pain in the *** to patch a tire on the side of the road because it will undoubtedly happen when you don't have the time or the patience to do it.
That leaves option number two: Call a tow truck. This will be fun getting your car towed home because of a flat. Again, on your way to somewhere...
Option three: Call the wife and have her grab the spare tire and a jack out of the garage, load them into the "grocery getter", and then drive them out to you. Once she gets there, you get to explain to her that the reason you don't have the spare tire in the car is that you're pretty sure that the weight reduction has taken like a billionth of a second off of your quarter mile time and that you've picked up a solid 1/10th of a mile per gallon increase in your fuel economy.
Leave the spare in the trunk
And make sure that it has air in it!