Learn Arabic (Modern Standard): سافرت إلى المدينة أمس.

أمس is an adverb of time. Unlike many nouns that change their final vowel based on their role in the sentence, أمس is fixed. It always ends with a "kasra" (an "i" sound, pronounced "amsi").

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

It is attached to the verb! In the Arabic past tense, the person doing the action is added as a suffix. The ـتُ (-tu) at the end of سافرت (sāfartu) means "I".

What effect does the preposition إلى (to) have on the word المدينة (the city)?

Nouns that directly follow prepositions like إلى take what is called the "genitive" case. For now, just remember that this means المدينة gets a "kasra" (an "i" sound) added to its final letter, making it sound like "al-madīnati".

Is the word المدينة related to the holy city of Medina?

Yes! The Arabic word مدينة simply means "city". When you add the definite article الـ (the) to make it المدينة, it means "the city". The famous city in Saudi Arabia is named exactly this, literally translating to "The City".