Learn Hardcore German: Unsere Unterkunft befindet sich nah am Bahnhof. - Our accommodation is close to the train station.

Unsere Unterkunft ist nah am Bahnhof. – grammatically OK, but a bit bare.
Unsere Unterkunft befindet sich nah am Bahnhof. – sounds more natural and specific for talking about location.

Nuance:

sein (ist) = very general “to be.”
sich befinden = specifically about the location of something, often used in descriptions (brochures, information texts, directions, etc.).

So befindet sich is simply more idiomatic when you talk about where a building/place is.

What is the role of sich in befindet sich? Is this always necessary?

Yes, sich is necessary here.

sich befinden is a reflexive verb in German.
It is almost always used with the reflexive pronoun sich:
- Ich befinde mich …
- Du befindest dich …
- Er/Sie/Es befindet sich …
- Wir befinden uns …
- Ihr befindet euch …
- Sie befinden sich …

Without sich, befinden normally has a different meaning (“to decide / judge something as …”), which is less common and more formal:

Das Gericht befindet ihn für schuldig. – “The court finds him guilty.”

In the location sense (“to be located”), you must use sich befinden.

Why is the word order befindet sich and not sich befindet?

In a normal main clause, German verb placement rules are:

The finite verb (here: befindet) must be in 2nd position.
Pronouns like sich go right after the finite verb unless something is moved to the front.

So:

Unsere Unterkunft – 1st idea (subject)
befindet – 2nd element (finite verb)
sich – reflexive pronoun after the verb
nah am Bahnhof – rest of the sentence

You could also say:

Nah am Bahnhof befindet sich unsere Unterkunft.

Here Nah am Bahnhof is in first position, so befindet still stays in 2nd, and sich again follows the verb.

Why is it unsere Unterkunft and not unser Unterkunft?

Because Unterkunft is feminine in German:

die Unterkunft – the accommodation

The possessive unser- must agree with the gender, number, and case of the noun:

Nominative feminine (singular): unsere Unterkunft
Nominative masculine: unser Bahnhof
Nominative neuter: unser Hotel
Nominative plural: unsere Unterkünfte

In the sentence, Unsere Unterkunft is the subject in nominative, so the correct form is unsere (feminine nominative).

Why is it nah am Bahnhof and not nah den Bahnhof or something else?

There are two things going on:

am = an dem
- Bahnhof is masculine: der Bahnhof.
- With location, an takes the dative: an dem Bahnhof.
- This contracts to am Bahnhof (very common in German).
nah is used with a prepositional phrase expressing location:
- nah am Bahnhof = near the station (literally: near at-the station).

Using nah den Bahnhof would be wrong because:

You need a preposition (an, bei, in der Nähe von, etc.).
For a static location, an takes the dative, not accusative.

What is the difference between nah, nahe, and in der Nähe von?

All three express “near / close to,” but they differ in style and structure.

nah (more colloquial, everyday)
- Often followed by a preposition:
  - nah am Bahnhof
  - nah beim Park
- As an adjective before a noun (with endings):
  - ein naher Verwandter – a close relative
nahe (a bit more formal/literary)
- Common structure: nahe + Dative:
  - nahe dem Bahnhof
- You can also hear nahe am Bahnhof, similar to nah am Bahnhof.
in der Nähe von (very common, neutral)
- Literally “in the vicinity of”:
  - Unsere Unterkunft liegt in der Nähe von dem Bahnhof.
    → usually … in der Nähe des Bahnhofs.

In your sentence, nah am Bahnhof is natural, conversational German.

Why is it am Bahnhof and not im Bahnhof, zum Bahnhof, or beim Bahnhof?

All of these exist, but they mean slightly different things:

am Bahnhof (an dem Bahnhof) – “at/by the station,” focusing on the general area right at the station.
im Bahnhof (in dem Bahnhof) – inside the station building.
zum Bahnhof (zu dem Bahnhof) – “to the station,” indicates movement towards it.
beim Bahnhof (bei dem Bahnhof) – “by/near the station,” often also OK instead of am, but sounds a bit more like “in the vicinity of the station” rather than right at it.

In the sentence, the idea is “Our accommodation is near the station”, so am Bahnhof fits best for a static location near that point.

Could I also say Unsere Unterkunft ist nah am Bahnhof?

Yes, this is grammatically correct and understandable.

However, native speakers more often say:

Unsere Unterkunft befindet sich nah am Bahnhof.
Unsere Unterkunft liegt nah am Bahnhof.
Unsere Unterkunft liegt in der Nähe des Bahnhofs.

Using ist nah is not wrong, but liegt or befindet sich sound more idiomatic when describing the location of a building or place.

What case is Bahnhof in, and why?

Bahnhof is in the dative singular:

Basic form (nominative): der Bahnhof
Dative singular: dem Bahnhof
With an (location): an dem Bahnhof → contracted to am Bahnhof

Reason:

The preposition an can take accusative (movement to) or dative (location at).
Here we talk about a fixed location (where something is), so we use dative:
- nah am Bahnhof = “near at the station” → static location → dative.

Is nah in this sentence an adjective or an adverb, and why doesn’t it have an ending (nahe, nahem, etc.)?

In Unsere Unterkunft befindet sich nah am Bahnhof, nah functions as an adverb / predicative adjective:

It describes how / where the accommodation is located relative to the station.
In this position (after the verb, not directly before a noun), German adjectives usually do not take endings.

Compare:

Ein naher Bahnhof – here naher is an attributive adjective before a noun, so it takes an ending.
Der Bahnhof ist nah. – here nah is predicative, no ending.
Unsere Unterkunft befindet sich nah am Bahnhof. – same situation: predicative, so no ending.