Identify the object of the preposition. My plan today is to study and then take a walk bu the river.

I believe the answer to be "the river".

Explanation:

The object of a preposition can be a noun, a noun phrase, or a pronoun that comes right after it and completes the preposition's meaning. In the sentence we are studying here, the preposition by indicates location and its meaning is completed by the words "the river" - article + noun.

Note: even though "to" can be a preposition as well, in this sentence it is used to show that the verb "study" is in its infinitive form.

the object is plan to the?