Hello there,
Some great day trips to make from Tokyo include.
Kamakura - visit the great Buddha and local temples. There are also nice beaches close by and woods to make great hikes.
Nikko - Visit the mausoleum of Shogun Tokugawa Ieyas, the area itself is also very beautiful and has much to offer.
Yokohama, Tokyo's twin in the Kanto region, this is an other big city. With much to explore and visit.
The Pasmo card is a prepaid travel card, that does not give any discount by itself. While the JR Pass basically is an all you can travel ticket for a set amount of time. Depending on the rest of your itinerary, a JR Pass works best if you can make savings with it. Otherwise buy a Pasmo card or just normal train tickets.
Hope this helps,
Daniel