I know it's possible to buy a 3-day metro pass at Tokyo airport but I missed that opportunity. Is it possible to still buy it in the center, preferably in the Asakusa area?
According to the Tokyo Metropolitan Subway website, the only places that the 3-day pass ("Tokyo Subway 3-Day Ticket") is available in the Tokyo metropolitan area are Haneda and Narita airports and Bic Camera (Yurakucho, Shinjuku, Akasaka Mitsuke, Ikebukuro, Shibuya East, Shibuya Hachiko, Shinjuku East, Shinjuku West, and Sofmap Akihabara).
If you buy it at Bic Camera, you will have to show your passport in order to prove that you are eligible.
If you are in Asakusa, the nearest would be the Sofmap Akihabara store or the Bic Camera Akasaka Mitsuke store.
An alternative option is the Pasmo/Suica. I 'lived' in Tokyo for 6 days because it was just a short visit. What I found really useful was the Pasmo (blank card). A prepaid card which you can put money into it and use it to travel around on public transport around the metropolitan area of Tokyo (this is what I did) It's great because there are many 'stations' to load more credit on. The initial payment is 500 yen (deposit).
For your reference, I've added a link for more information. http://www.pasmo.co.jp/en/buy/