Yes, Shibuya area is a nice place! You can take some subway / train lines from Shibuya station and these bring you to residential area soon with some stops. I hope there are some Airbnb rooms. ( actually I’m not a user of Airbnb....I’m not so sure)
Ebisu or Daikanyama is one of the most popular area among foreigners. It’s also close to Shibuya.
How about Shimokitazawa?
It’s nice area and popular among young people. There are lots of casual shops.
Roppongi is the most popular area among visitors but there are less accommodations and it’s too expensive. You’d better spend time just for fun.
Regarding east area, There are many guest houses in Asakusa and Kuramae area. But there are less young people. You can take subway and easy to get to Shibuya or other fun places.