Često se sjećam prvog dana u Zagrebu, dok se moja sestra radije sjeća našeg prvog izleta na more.

Because Croatian usually leaves subject pronouns out when the verb ending already makes the subject clear.

• sjećam = I remember
• sjeća = he/she remembers

So Često se sjećam... already means I often remember...
You would add ja only for emphasis or contrast, for example: Ja se često sjećam..., a moja sestra...

Se is part of the verb sjećati se. In this verb, it is not optional.

The dictionary form is sjećati se = to remember.
So:

• sjećam se = I remember
• sjeća se = he/she remembers

English does not need anything extra here, but Croatian does. You normally cannot just say sjećam by itself with this meaning.

Because sjećati se takes the genitive case.

So the thing you remember must be in genitive:

• prvi dan → prvog dana
• prvi izlet → prvog izleta

The possessive/adjective words also have to match the noun in case, gender, and number:

• naš prvi izlet → našeg prvog izleta

So the case change is not random; it is required by the verb sjećati se.

It is locative singular.

With u:

• u + locative = being in a place
• u + accusative = movement into a place

Here the meaning is location, not movement, so Croatian uses u Zagrebu = in Zagreb.

Compare:

• Živim u Zagrebu. = I live in Zagreb.
• Idem u Zagreb. = I’m going to Zagreb.

Because na more is the normal Croatian expression for to the seaside / to the coast / on a seaside holiday.

So:

• izlet na more = a trip to the seaside

But:

• u more literally means into the sea

That is why na more is correct here. It refers to the destination as a seaside place, not physically going into the water.

Here dok means while or whereas.

In this sentence it has a slightly contrastive feel:

• I often remember the first day in Zagreb, whereas my sister prefers to remember our first trip to the seaside.

So dok can connect two actions happening in parallel, but it can also highlight a contrast between two people or situations.

Radije means rather or preferably, and with a verb it often corresponds to English prefer to.

So:

• moja sestra radije se sjeća... means
• my sister would rather remember... / prefers to remember...

It is the comparative form of rado, but in everyday use you can simply think of radije as rather / prefer.

Because se is a clitic, and Croatian clitics usually go in the second position in the clause.

So:

• Često is first → se comes next
• dok is first → se comes next

That is why the sentence has:

• Često se sjećam...
• dok se moja sestra radije sjeća...

This is very normal Croatian word order. Clitics often come early, not necessarily directly before or after the main verb the way an English speaker might expect.

Because the sentence is not describing the past event itself. It is describing the present or habitual act of remembering.

So:

• sjećam se = I remember / I often remember
• sjeća se = she remembers / tends to remember

The events happened in the past, but the act of recalling them happens now, or happens repeatedly.

This is a common aspect pair:

• sjećati se = imperfective
• sjetiti se = perfective

In simple terms:

• sjećati se focuses on remembering as a state, process, or repeated action
• sjetiti se focuses on the moment of recalling something

So in this sentence, sjećati se fits because the meaning is habitual: I often remember..., my sister prefers to remember...

Example contrast:

• Često se sjećam djetinjstva. = I often remember childhood.
• Odjednom sam se sjetio njezina imena. = I suddenly remembered her name.

Yes, in other contexts prvog dana can mean on the first day as a time expression.

For example:

• Prvog dana smo obišli grad. = On the first day we toured the city.

But in your sentence, prvog dana is the object of sjećam se, so it means the first day as the thing being remembered.

So the form is the same, but the function is different. Context tells you which meaning is intended.