Gogolya st
This is nice alley with two lines of old chestnut trees on both sides. Gives you nice quiet walk in summer and fall.
The Fortress of Brest PL: BrzeÅÄ Litewski preserves the ruins of a massive fortification built in XIX century by Russian Empire, that achieved "Hero Fortress" status during World War II. Admission fee. Walking the grounds of this great fortification is a moving experience that gives a good sense of the privations faced by the forces that were besieged there. There is a museum, where you can learn about fight between attacking Germans and defending Soviets. There is also small part about Polish defenders of this place, who were attacked earlier by Germans and Soviets. The history of Brest Fortress is complicated, as you can see, and worth learning.
Naberezhnaya
If you just happen to wander around the city this is my best place, especially late summer - fall. The riverfront has a lot of willow trees and there are a lot of ducks swimming in the river. There are some chairs under the willow trees sitting on which is very relaxing.