Vaya donde vaya, mi hermana siempre busca un sitio donde sirvan gazpacho o una buena ensalada.

It means wherever she goes or no matter where she goes.

This is a very common Spanish pattern for expressing free choice or it doesn’t matter where/how/what. So the sentence begins with the idea:

Wherever she goes, my sister always looks for a place...

The subject is understood from the rest of the sentence: mi hermana.

Spanish often uses the pattern:

subjunctive verb + relative word + same subjunctive verb

So:

• vaya donde vaya = wherever she goes
• pase lo que pase = whatever happens
• sea como sea = however it may be

It may look repetitive to an English speaker, but in Spanish it is a normal structure.

Because this construction expresses indefiniteness and concession: it does not refer to one specific place she goes to, but to any place at all.

So Spanish uses the subjunctive in structures like this:

• Vaya donde vaya = no matter where she goes
• Haga lo que haga = no matter what he/she does

Using va donde va would not give the same meaning and would sound wrong here.

Because here donde is a relative adverb, not a question word.

Use an accent in questions or indirect questions:

• ¿Dónde está?
• No sé dónde está.

No accent in relative clauses:

• Voy donde tú vayas.
• Vaya donde vaya...

So in this sentence, donde means where/wherever, not where?

Yes, with verbs of movement, adonde is possible in many cases. So Vaya adonde vaya can also exist.

That said, Vaya donde vaya is very natural and common. In everyday Spanish, donde is often used even with movement verbs.

Because Vaya donde vaya is an introductory subordinate clause.

In English, you would also normally write:

Wherever she goes, my sister...

Spanish commonly separates this kind of opening clause with a comma, so the punctuation here is standard.

Because the place is not specific or known. She is looking for any place that serves gazpacho or a good salad.

Spanish often uses the subjunctive after words like un sitio, un lugar, alguien, algo when the thing is indefinite, unknown, or only desired:

• Busco un libro que sea interesante.
• Necesitamos un hotel que tenga piscina.
• Busca un sitio donde sirvan gazpacho.

If it were a specific, known place, Spanish would usually use the indicative:

• Busco el sitio donde sirven gazpacho.

That suggests the speaker has a particular place in mind.

Because sitio is not the subject of sirvan.

The understood subject is something like they:

• un sitio donde sirvan gazpacho = a place where they serve gazpacho

Spanish often leaves that subject unstated because it is obvious from the context. So sirvan is plural because it means where they serve.

Normally, no, not in this sentence.

Sirva would be singular, but the natural idea here is where they serve gazpacho, not where the place serves gazpacho.

Spanish usually prefers:

• un sitio donde sirvan...

rather than making sitio act like the thing doing the serving.

Because she is not looking for one specific, already identified place. She is looking for any suitable place.

So:

• un sitio = any place / a place
• el sitio = the place / a specific place

This matches the use of the subjunctive in donde sirvan.

Because gazpacho is being treated as an uncountable food item here, while ensalada is countable.

So:

• sirvan gazpacho = serve gazpacho
• sirvan una buena ensalada = serve a good salad

This is similar to English:

• serve soup
• serve a good salad

If you wanted to make gazpacho more countable or specific, you could say something like un buen gazpacho, but that is not what this sentence is doing.

It means or a good salad as an alternative.

So the idea is that she looks for a place where they serve:

• gazpacho
• or a good salad

It does not necessarily mean she wants both. It means either option would satisfy what she is looking for.

Yes, lugar would also be possible.

• un sitio donde sirvan gazpacho
• un lugar donde sirvan gazpacho

Both mean a place where they serve gazpacho.

In many contexts, sitio feels a bit more everyday and conversational, while lugar can sound a little more neutral or formal. But both are correct.