Cato the Elder is traditionally thought to be anti-Greek. He wrote a history in Latin because he believed his son should have a Roman history of Rome and not that drivel the Greeks were writing.

That position is now being reevaluated starting with Astin's biography in 1978. Astin (if I remember correctly - I don't have the book on hand) showed Cato receptive to a number of Greek influences, including the notion of writing a history in the first place.

Aside from that, satire is sometimes spoken of as a uniquely Roman form, but that's not really a rejection of Greek ideas as much as propagation of Roman ones.

In the late Roman republic there was considerable backlash against Greek ideas. The opinion of these was that Greek ideas were a reversal of traditional Roman values. Cato the Elder opposed the onset of Greek culture, Plutarch Life of Cato the Elder 22 says "The other Romans were pleased at this, and glad to see their young men lay hold of Greek culture and consort with such admirable men. But Cato, at the very outset, when this zeal for discussion came pouring into the city, was distressed, fearing lest the young men, by giving this direction to their ambition, should come to love a reputation based on mere words more than one achieved by martial deeds."

The desire for Roman traditions comes out in mostly as an opposition against the corruption of eastern luxury. You can see it in the Augustan marital legislation, in Juvenal's satires, or in the hostility to the emperor Elagabalus.