All of the sentences provided contain both a noun phrase and a verb phrase.
- In the first sentence, "He" is the noun phrase and "sat on my grandmother’s favorite armchair" is the verb phrase.
- In the second sentence, "Some dog breeds" is the noun phrase and "have docked tails" is the verb phrase.
- In the third sentence, "The pigeons" is the noun phrase and "have not landed on my neighbor’s balcony in a long time" is the verb phrase.
- In the fourth sentence, "You" is the noun phrase and "can find frogs and insects by the pond if you look closely enough" is the verb phrase.
Thus, any of the sentences would be correct.