1. The Farmer's Market at United Nations University
It's an easy trip in between checking out Meiji Jingu shrine, shopping along Omotesando, and walking the busy crosswalk of Shibuya! You can check out on their facebook page what event is going on the weekend you are visiting :)
2. Akasaka Nominoichi (Flea Market) in Ark Hills
A good place to start your day before grabbing lunch and heading to Roppongi to do some shopping or visit any of the following museums: Mori Art Museum, 21_21 Design Sight museum, National Art Center, and/or Suntory Museum of Art.
3. Oedo Kottoichi (Antique Market) in Yoyogi Park/Yurakucho
Tokyo International Forum: Every 1st and 3rd Sunday of the month, 9am to 4pm
Yoyogi Park: irregularly*
*Check out the official website, or the facebook page specifically for Yoyogi Park.
Tokyo International Forum: 1 min walk from Yurakucho station, 5 min walk from Tokyo station
Yoyogi Park: 8 min walk from Harajuku station
Yurakucho is minutes away from Ginza, famous for the shopping district with luxury fashion brands, as well as being the home to flagship store of Ginza Itoya, the 100 year old stationary shop!