Sophisticated renovation on the best block in the city. Grand, tree-lined street facing the Museum of Natural History, steps from Central Park, the subway, and services on Columbus Ave. This cleanly designed apartment is in a 12-story pre-war, mid-block apartment building, a front row seat for the Macy's Day Parade and inflating the spectacular parade balloons Thanksgiving Eve.   Apartment 9F is a highly efficient space with a designer's-eye level of finish. Great studio room with 10' ceilings and custom built-ins. Bright and super clean, the extensive renovation features refinished walls, original oak floors and a state-of-the-art kitchen with marble counter tops, under-counter lighting and European-grade appliances. Glass brick backsplash plays off the maple cabinetry in a very pleasing color palette. The upgraded electric and designer lighting throughout the apartment support an executive-level home office. Double-hung closets ensure there's plenty of space for all your belongings.     35 West 81st Street is a boutique cooperative building in every sense of the word. Gracious 24-hour door staff and live-in super oversee all your needs. Building offers onsite laundry, bike room, gym and roof deck. Pieds--terre are welcome. Parents buying for children is allowed and with the B/C train right on the corner, it's an easy commute into Midtown, Julliard as well as Columbia University.