Learn Croatian: Danas tražim miran park. - Today I am looking for a peaceful park.

Because park is a masculine inanimate noun (it is a thing, not a living being). In Croatian, when a masculine noun is inanimate, its accusative form and the adjectives attached to it look exactly like their basic dictionary (nominative) forms. So, miran park does not add any new endings.

Why is miran park in the accusative case here to begin with?

Because it is the direct object of the verb tražiti (to look for). The thing you are looking for receives the action of the verb, which means it must be put into the accusative case.

Where is the word for 'I' in this sentence?

The verb tražim already has the -im ending, which means 'I am looking for'. Since the verb ending tells us exactly who is doing the action, the pronoun ja (I) is usually left out unless you want to add special emphasis.

Can I move the word Danas to the end of the sentence?

Yes, Croatian word order is quite flexible. You could say Tražim miran park danas. Putting Danas at the very beginning just places a little more focus on the fact that you are looking for it today.