Unlike some other languages, it is not uncommon in English to separate verb (remember) from adverb (best) in a sentence. So, the most natural-sounding option is, "I remember this city best."
Please note that your two example sentences are in different tenses. The first one, with 'remembered', is past tense. The other one, with 'remember', is present tense. However, this difference does not change the best option.
You could say, "I remember best this city." This construction keeps the verb + adverb together, and sounds more natural to me than the example you gave. However "I remember this city best" still sounds more natural.