The climate in Boston varies with the seasons with very snowy winters and sweltering summers when hot sidewalks could damage puppy paws. Check the weather before you go out as there is a chance you could be caught in a snow storm!
As Fenway was named after a parkland, there's no question there's plenty of greenery around the area. There are many trees and grassy spots outside apartment buildings as well as parks throughout the neighborhood. The streets around Fenway Park have the least green space and can become very crowded with tourists and university students during baseball season and weekend afternoons or nights. The best time to walk near Fenway is in the morning.
Justine Mee Liff Park is a traditional park on the Emerald Necklace featuring grassy spaces and shady spots to sit and relax. Instead of exploring the Emerald Necklace, you can also check out Ramler Park, a small park dedicated to creating a sanctuary for migrating birds.