Last August Washingtonians were treated to a taste of Chekhov at the Kennedy Center, which hosted the Sydney Theater Company’s production of Uncle Vanya, starring the ever-lovely Cate Blanchett as wife Yelena and intense Hugo Weaving as the husband, Astrov. (The ultimate Lord of the Rings elfin power couple!) Now, New Yorkers will get a taste of their own — next summer’s Lincoln Center Festival just announced a five-week run for Blanchett and Weaving.