There are two places my co-workers and I go to for a leisurely lunch when it's beautiful out...
Suji's in Azabudubai for brunch or anything off their New York grill menu. (The portions are American so pace yourself...or ask for a doggy bag). www.sujis.net
Macchinesti Coffee (azabu juban branch) has a sunken terrace on a quiet street. Their marinated chicken takes about a half hour to arrive at your table but is just about the best thing I've ever eaten.
(These terrace tips are top secret so shhh....)
Both Tokyo Midtown and Roppongi Hills have several restaurants with outdoor seating. At Midtown there's Botanica (the new Conran restaurant), Nirvana New York, Union Square Tokyo, a branch of Fonda de la Madrigada Mexican restaurant, and a few others.
Also, both branches of Aux Bacchanales (Tameike and Kioicho), Bistrot d'Artemis (Yoyogi), Pierre Gagnaire a Tokyo (Omotesando), Antwerp Central (Marunouchi), and many more.
Canal Cafe (in the photo) is one of my favorites, except during mosquito season.