Gardens

Hello Karla!
-I Personally recommend the Shinjuku Gyoen National Garden https://planetyze.com/en/japan/tokyo/shinjuku-gyoen
-And also the The Imperial Palace East Gardens is definitely my favorite, I love that place! https://planetyze.com/en/japan/tokyo/the-imperial-palace-east-gardens
-There's also the Hamarikyu Gardens: https://planetyze.com/en/japan/tokyo/hamarikyu which you can go by boat from asakusa and then visit Odaiba afterwards, its a nice ride and a beautiful garden where you can also have a tea ceremony.

For other gardens in Tokyo, search for these:
Rikugien Garden, 
-Koishikawa Korakuen Garden, 
-Kiyosumi Garden, 
-Kyu Shiba Rikyu Garden, 
-Mukojima-Hyakkaen Garden and 
-Tonogayato Garden

And if you go to visit Kamakura during you trip, you can also visit the famous gardens outside Hasedera temple: https://planetyze.com/en/japan/kamakura/hasedera-temple

I hope this helps :-)