Learn Hardcore Polish: W przyszłym roku chciałbym spędzić urlop w Hiszpanii. - Next year I would like to spend my vacation in Spain.

The preposition w meaning “in” (where? / when?) normally takes the locative case.
rok in locative is roku.
The adjective przyszły (“future / next”) in masculine singular locative is przyszłym.

So you get:

w + przyszłym + roku = in next year → w przyszłym roku

If you said w przyszły rok, that would be accusative, which is used with w for movement into something (e.g. w przyszły rok wejść = to enter the next year), not for stating when something happens. For time expressions with w, you generally use the locative:
w tym roku, w zeszłym roku, w przyszłym miesiącu etc.

What is the difference between przyszłym and następnym (as in w przyszłym roku vs w następnym roku)?

Both can mean “next” and in this sentence they’re practically interchangeable:

w przyszłym roku – in the coming year, the future year.
w następnym roku – in the following year (the one that comes after the current one or after some other reference point).

Nuance (not always important in everyday speech):

przyszły tends to point more to “the future” as such.
następny is more “the one after this one / the next in a sequence”.

In everyday conversation, w przyszłym roku is the most standard phrase for “next year”; w następnym roku is also correct and natural.

Why is chciałbym used instead of chcę?

Both come from chcieć (“to want”), but:

chcę = “I want” (present tense, direct, can sound a bit blunt).
chciałbym = literally “I would want / I would like” (conditional, more polite and softer).

In Polish, the conditional form chciałbym is very common when:

expressing wishes: Chciałbym spędzić urlop w Hiszpanii – I’d like to spend my vacation in Spain.
being polite/less direct: Chciałbym kawę – I’d like a coffee.

Using chcę here:

W przyszłym roku chcę spędzić urlop w Hiszpanii is correct and means I want to spend my vacation in Spain next year, but it sounds more firm/decided and less “polite wish”, more like a plan or a strong intention.

How does gender work in chciałbym? What if the speaker is female?

The form chciałbym is masculine first person singular conditional.

Structure:

chciał- – past stem of chcieć (masculine: chciał; feminine: chciała).
by – conditional particle.
m – ending for 1st person singular.

So:

A man says: chciałbym (I would like).
A woman says: chciałabym (I would like).

Other examples:

Chciałbyś / chciałabyś – you (sg.) would like (to a man / to a woman).
Chciałby / chciałaby – he would like / she would like.

In your sentence, if a woman is speaking, you’d say:

W przyszłym roku chciałabym spędzić urlop w Hiszpanii.

Can bym be written as a separate word, like ja bym chciał spędzić…?

Yes, grammatically it can be separated, and this happens quite a lot in speech:

Ja bym chciał spędzić urlop w Hiszpanii.
Ja bym chciał w przyszłym roku spędzić urlop w Hiszpanii.

However, the standard written form when the conditional particle attaches to the verb is one word:

chciałbym, zrobiłbym, poszedłbym, etc.

When you move by(m) away from the verb (for emphasis or style), you write it separately:

Ja bym chciał…
Ja bym to zrobił.

Meaning is essentially the same; moving bym can slightly change rhythm/emphasis.

Why is there an infinitive spędzić after chciałbym?

In Polish, after verbs like chcieć (“to want”), you normally use the infinitive:

chcę spędzić – I want to spend
chciałbym spędzić – I would like to spend
muszę spędzić – I must spend
mogę spędzić – I can spend

So chciałbym spędzić directly parallels English “I would like to spend”:

chciałbym – I would like
spędzić – to spend

Why is it spędzić and not spędzać? What is the aspect difference?

Polish verbs have aspect: perfective vs imperfective.

spędzić – perfective: to spend (time) as a single, completed event.
spędzać – imperfective: to spend (time) in a repeated / ongoing / habitual way.

In your sentence, you’re talking about one specific future vacation, so the perfective form fits best:

W przyszłym roku chciałbym spędzić urlop w Hiszpanii.
→ I’d like to (completely) spend that one vacation in Spain.

If you say:

Chciałbym spędzać urlop w Hiszpanii.
that suggests a habit or a general preference:
I’d like to (generally) spend my vacations in Spain (every year, usually, etc.).

What exactly does urlop mean, and why not wakacje?

Both relate to time off, but they aren’t identical:

urlop – leave from work, vacation time granted to an employee.
- Typical translation: vacation / leave (from a job).
- Ex.: Jestem na urlopie. – I’m on vacation (off work).
wakacje – (usually) school or university holidays (often summer), or holidays in general.
- Ex.: Dzieci mają wakacje. – The children are on holiday.

In your sentence, urlop suggests:

you are a working person talking about your annual leave or time off from work.

If you said:

W przyszłym roku chciałbym spędzić wakacje w Hiszpanii.
it would be understood as “I’d like to spend the holidays in Spain,” often with a school/university vibe or just general holidays, not specifically work leave.

What case is urlop in here, and why that form?

Urlop in this sentence is in the accusative singular.

Base form (nominative): urlop.
Accusative singular for a masculine inanimate noun is the same: urlop.

It’s in accusative because it’s the direct object of the verb spędzić:

spędzić (co?) urlop – to spend what? vacation.

So:

spędzić urlop = to spend (your) vacation.

Why is it w Hiszpanii and not do Hiszpanii?

Different prepositions express different relations:

w Hiszpanii – in Spain (location: where you are).
do Hiszpanii – to Spain (direction: where you are going).

Your sentence focuses on where you will spend your vacation, i.e. your location during that time:

spędzić urlop w Hiszpanii – spend your vacation in Spain.

If you wanted to stress the trip or direction, you might say something like:

W przyszłym roku chciałbym pojechać do Hiszpanii na urlop.
– Next year I’d like to go to Spain on vacation.

What case is Hiszpanii, and why is that form used after w?

Hiszpanii is the locative singular of Hiszpania (Spain).

Declension:

Nominative: Hiszpania (subject form).
Locative: Hiszpanii (used mainly after certain prepositions, including w = in).

Preposition w:

When it means “in” (where?), it generally takes the locative.
- w Polsce, w Niemczech, w Hiszpanii – in Poland, in Germany, in Spain.

So:

w (gdzie?) Hiszpanii → “in Spain”
hence w Hiszpanii.

Can the word order in this sentence be changed?

Yes, Polish word order is relatively flexible. Your version:

W przyszłym roku chciałbym spędzić urlop w Hiszpanii.

Other natural variants:

Chciałbym w przyszłym roku spędzić urlop w Hiszpanii.
Chciałbym spędzić urlop w Hiszpanii w przyszłym roku.
Urlop chciałbym w przyszłym roku spędzić w Hiszpanii. (emphasises urlop)

All of these are correct. The differences are mostly about emphasis and rhythm, not grammar:

Elements brought earlier are often more topical or emphasised.
Neutral and very common is your original order or:
W przyszłym roku chciałbym spędzić urlop w Hiszpanii.

How would I say a more definite future statement, like “I will spend my vacation in Spain next year”, instead of “I would like to…”?

You can switch from the conditional chciałbym (“I’d like to”) to a future form of spędzić:

W przyszłym roku spędzę urlop w Hiszpanii.
– Next year I will spend my vacation in Spain.

Notes:

spędzę is the simple future (perfective) of spędzić, used for a single, completed future action.
You can still move phrases around:
- Urlop w przyszłym roku spędzę w Hiszpanii.
- W Hiszpanii spędzę urlop w przyszłym roku.

All keep the same basic meaning: a firm plan/prediction, not just a wish.