Pater respondet Spartam clarissimam fuisse, sed se potius Syracusas visere velle.

Because Latin usually reports statements with an accusative + infinitive construction instead of a separate word like English that.

So after respondet, the reported content is:

• Spartam clarissimam fuisse
• se potius Syracusas visere velle

English says He answers that..., but Latin often just uses this infinitive construction with no extra word.

They are accusative because they belong to an indirect statement.

In Latin indirect statement:

• the subject of the reported clause goes into the accusative
• the verb goes into the infinitive

So:

• direct statement: Sparta clarissima fuit / est
• indirect statement: Spartam clarissimam fuisse

Also, clarissimam describes Spartam, so it must agree with it in:

• gender: feminine
• number: singular
• case: accusative

Fuisse is the perfect infinitive of esse.

In indirect statement, the tense of the infinitive shows time relative to the main verb:

• esse = to be, being at the same time
• fuisse = to have been, being earlier
• fore / futurum esse = to be going to be, later

So Spartam clarissimam fuisse means that Sparta had been / was very famous.

In smoother English, this is often just translated that Sparta was very famous, even though Latin is showing prior time with fuisse.

Grammatically, clarissimam is the superlative of clarus, so it can mean:

• most famous
• very famous
• most renowned

In many Latin sentences, a superlative is used in an intensive sense, not necessarily as a strict comparison. So here very famous or most renowned may both be possible depending on context.

Se is a reflexive pronoun, and here it refers back to pater.

So:

• pater respondet ... se ... velle
• = the father answers that he wants...

The he is the same person as pater, so Latin uses se.

If it referred to some other male person, Latin would use eum, not se.

For the same reason as fuisse: this is still indirect statement.

The direct version would be something like:

ego potius Syracusas visere volo

When that becomes reported speech after respondet, volo changes to the infinitive velle, and ego changes to se:

• direct: ego ... volo
• indirect: se ... velle

So se potius Syracusas visere velle means that he would rather visit Syracuse.

Visere depends on velle.

So the structure is:

• velle = to want
• visere = to visit / go to see

Together:

• se Syracusas visere velle
• = that he wants to visit Syracuse

So velle is the main infinitive of the indirect statement, and visere is its complementary infinitive.

Because Syracusae is a city name that is plural in form in Latin.

Its cases are like this:

• nominative: Syracusae
• accusative: Syracusas

Here it is accusative because it is the object of visere:

• Syracusas visere = to visit Syracuse

So even though English treats Syracuse as singular, Latin uses the plural form Syracusae / Syracusas.

Potius means rather.

It shows preference or contrast:

• Spartam clarissimam fuisse = Sparta was very famous
• sed se potius Syracusas visere velle = but that he would rather visit Syracuse

So the father is not denying Sparta's fame; he is saying that his preference is to visit Syracuse instead.

Visere often means to go to see, to visit, or to look at, and it is a very natural verb for visiting a place.

By contrast, videre more basically means to see.

So:

• videre = to see
• visere = to visit / go see

In this sentence, visere is exactly the right idea for traveling to a city.

A natural direct version would be:

Sparta clarissima fuit, sed ego potius Syracusas visere volo.

Then, when it is reported after pater respondet, Latin changes it into indirect statement:

• Sparta → Spartam
• clarissima → clarissimam
• fuit → fuisse
• ego → se
• volo → velle

That gives:

Pater respondet Spartam clarissimam fuisse, sed se potius Syracusas visere velle.