Libertarianism is fiscally on the right. In terms of civil issues, it's on the left.
Libertarianism is all about open markets... letting the market regulate itself, having no government say on anything related to wealth, taxes, and distribution of wealth. Libertarians usually side with Republicans in terms of tax cuts, loosening of regulations, and establishing a pro-business front (which is why I don't like Paul).
At the same time, libertarianism is about you picking your poison. Want to smoke pot? Go ahead, it's your choice! Want to drive your bike with no helmet? Your choice. You have an accident and die, no one to blame but yourself. Gay rights? Sure, they can do what they want! Immigration? People are free to move (though Paul's stance is an unusual one). War on crime? That's too much government power. War on drugs? Too much money, too many deaths. Not working. War on terror? What is terror? Just a bs term invented to intervene in someone else's sovereignty. This, for me, is Paul's good side.
Ambiguous, in terms of where to place him. In all honesty, I can't envision him in the middle, because that's where all the boring moderates are at. He's a schizophrenic extremist (in a good way) that shifts from left to right in ways that Democrats and Republicans are often too timid on doing. He is a little conservative, a little liberal. But scholars are more comfortable pooling him with fellow Republicans, particularly because of his distaste of the welfare state, and regulations.