The Republic is always worth reading as an allegory illustrating Plato's ideas of truth, justice and the good. It shouldn't simply be vilified, since it has much to teach us about those concepts. And a conservative thinker like Richard Weaver learned much from Plato's emphasis on the eternal values. There was an interesting recent thread on ten great books.
As you note, though, Plato's ideal country "does not mesh completely with American values." Indeed, there's much in the Republic that, taken as purely practical advice, would rightly repel us. I don't think we can or should simply throw out Plato. He's a vital link in the chain of Western ideas. But I do think Aristotle and other thinkers have more to teach us about practical political questions. I would to some extent agree that Plato can show us a vision of the common good, not found in many modern libertarians, but it's a vision that's already entered into our culture and found other theorists closer to us in their sentiments and loyalties.
What I notice in American conservatism is a recent movement away from the transcendent to the more practical. I don't think one can identify the transcendent wholly with Plato, but it would be a good idea to keep reading him so we don't lose touch with that side of our existence. It's not good to think that one can realize dreams, but also not so good for people to think they can stop dreaming or live wholly in the practical sphere.
Aristotle's Poetics is very important. See my FR homepage and some of my links there, you will see why...