I imagine that ROCOR (though I'm not certain) Western Rite priests, at least here in the states, would be trained at Holy Trinity Seminary/Monastery in Jordanville.
However, for Antiochians, the only other jurisdiction to offer western rite, they are trained at St. Tikhon's, St. Vlad's and Holy Cross. They are given education in EAstern Orthodox dogma and there are some classes in western rite liturgies, but I doubt it's comprehensive. As many of the Western Rite priests come from an Episcopalian, Lutheran or Catholic background, I don't think they have to be trained strictly in liturgics as they have that training already.
But I have heard something that may indicate a new seminary to be available for strictly western rite priests. Metropolitan JONAH has made numerous overtures to disenfranchised Episcopalians who have now formed the Anglican Church of North America (ACNA) and he recently gave a speech to a number of them in someplace in Wisconsin where a seminary is located. Now, keep in mind that all of this is speculative, there may be the chance that this particular seminary, in an agreement with the ACNA, may also train Orthodox WEstern Rite priests. If such is the case, I think there is cause for concern. WE don't send priests to be educated in Lutheran or Catholic seminaries. I don't care if the ACNA is close to Orthodoxy; they are not Orthodox, pure and simple. Again, all speculation, but if such thing were to achieve fruition, I think we are going to need another Bishop RAPHAEL to clean up the mess, no matter how good the intentions of Metropolitan JONAH are.