Learn Hardcore Icelandic: Á sunnudögum förum við stundum á lítið sveitasafn nálægt borginni. - On Sundays we sometimes go to a small rural museum near the city.

Á sunnudögum = On Sundays (in general, habitually)
Á sunnudaginn (accusative singular with the article) = On Sunday (this coming / that specific Sunday)
Á sunnudegi (dative singular, less common in modern speech for this meaning) can also mean on a Sunday in a more general or stylistic way.

Here we mean a repeated, habitual action, so Á sunnudögum is the natural choice.

Why does á take the dative in Á sunnudögum, but the accusative in á lítið sveitasafn?

The preposition á is “two-way”: it can govern dative or accusative depending on meaning.

With time expressions (like days of the week), á normally takes dative:
- Á sunnudögum – On Sundays
- Á föstudögum – On Fridays
With places, the rule is:
- Dative = location (“on / in” somewhere, no movement to it)
- Accusative = movement to somewhere

Examples:

Ég er á safninu. – I am at the museum. (dative: safninu)
Ég fer á safnið. – I go to the museum. (accusative: safnið)

In the sentence:

Á sunnudögum – time expression → dative plural (sunnudögum)
á lítið sveitasafn – movement to a museum → accusative (lítið sveitasafn)

What exactly does förum mean, and what is the base form of that verb?

Förum is the 1st person plural present tense of the verb fara (to go).

Basic forms of fara:

infinitive: fara – to go
ég fer – I go
þú ferð – you (sg.) go
hann/hún/það fer – he/she/it goes
við förum – we go
þið farið – you (pl.) go
þeir/þær/þau fara – they go

So förum corresponds to English “we go”. The vowel change a → ö is just part of the regular conjugation pattern for this verb.

Why is the subject við and not okkur?

Við and okkur are different cases of the same pronoun “we”:

við – nominative (subject form)
okkur – accusative/dative (object form)

Examples:

Við förum á safnið. – We go to the museum. (við = subject)
Kennarinn sér okkur. – The teacher sees us. (okkur = object)
Hann gefur okkur bók. – He gives us a book. (okkur = indirect object)

In the sentence Á sunnudögum förum við stundum á lítið sveitasafn, “we” is the one doing the action (we go), so the nominative form við is required.

Where can stundum go in the sentence, and does its position change the meaning?

Stundum means “sometimes” and is an adverb. In Icelandic, adverbs like this are fairly flexible, but there are preferred “natural” positions.

All of these are grammatically OK and mean essentially the same thing:

Á sunnudögum förum við stundum á lítið sveitasafn.
Á sunnudögum förum við á lítið sveitasafn stundum.
Á sunnudögum förum við á lítið sveitasafn stundum.

You could also move it further forward:

Stundum förum við á sunnudögum á lítið sveitasafn.

However, the most neutral, natural-sounding order is what you have:

Á sunnudögum förum við stundum á lítið sveitasafn.

Changing the position can slightly change what is being emphasized, but usually the basic meaning “sometimes” stays the same.

Why is it lítið sveitasafn and not lítill sveitasafn?

This is about gender and case agreement between the adjective and the noun.

safn is a neuter noun in Icelandic.
In the accusative singular indefinite, neuter adjectives end in -t.

So:

lítið safn – a small museum/collection (accusative or nominative neuter singular)
lítill is the masculine form (e.g. lítill hundur – a small dog)
lítil is the feminine form (e.g. lítil borg – a small town/city)

Because sveitasafn is also neuter, the adjective must agree:

á lítið sveitasafn – to a small country museum (accusative neuter singular)

So lítill sveitasafn would be ungrammatical; the genders don’t match.

Is sveitasafn one word or two, and what does it literally mean?

Sveitasafn is one word — a compound noun:

sveita- from sveit = countryside, rural area, a region outside the city
-safn = collection, museum

Literally, it’s something like “countryside-collection” or “rural museum”. In English you might say:

country museum
rural museum
local heritage museum (depending on context)

In Icelandic, forming compounds like this is very common, so instead of saying “museum in the countryside”, they prefer a single compound noun sveitasafn.

What does nálægt do in nálægt borginni, and why is borginni in that form?

Nálægt here is used as a preposition meaning “near / close to”. It governs the dative case.

borg – city, town (feminine noun)
borgin – the city (nominative, definite)
borginni – dative singular, definite form of borg

Because nálægt requires dative, we get:

nálægt borginni – near the city

So:

nálægt + dative:
- nálægt húsinu – near the house
- nálægt skólanum – near the school
- nálægt borginni – near the city

The ending -inni marks both dative and definiteness for this feminine noun.

Why is it nálægt borginni (“near the city”) but á lítið sveitasafn (“to a small museum”) without “the”? Why is one definite and the other indefinite?

This is about what is specific and known in the context.

á lítið sveitasafn – to a small country museum
- This suggests any small country museum, or one that hasn’t been clearly identified before in the conversation. It’s indefinite.
nálægt borginni – near the city
- Here “the city” is treated as known/specific from context. For example, the speaker and listener may already know which city they live near, so it naturally gets the definite form.

In Icelandic, definiteness is usually marked by a suffix on the noun:

borg – city
borgin – the city (nom.)
borginni – the city (dat.)

So the sentence means something like: On Sundays we sometimes go to a small country museum that is near the (known, specific) city.

Can the word order be changed, for example Við förum stundum á lítið sveitasafn á sunnudögum? Is that correct?

Yes, Icelandic word order is fairly flexible, especially for adverbials (time, frequency, place). Your version is grammatically correct:

Við förum stundum á lítið sveitasafn á sunnudögum.

Differences:

Á sunnudögum förum við stundum á lítið sveitasafn.
- Begins with the time expression, which is very common in Icelandic: “On Sundays, we sometimes go …”
Við förum stundum á lítið sveitasafn á sunnudögum.
- Begins with the subject, closer to English word order: “We sometimes go to a small rural museum on Sundays.”

Both are natural; starting with the time phrase (Á sunnudögum …) is particularly typical in Icelandic narrative or description.

Which words are in which cases in this sentence, and why?

Sentence: Á sunnudögum förum við stundum á lítið sveitasafn nálægt borginni.

Breakdown by case:

Á sunnudögum
- sunnudögum – dative plural of sunnudagur (Sunday)
- Reason: time expression with á → dative
förum við
- við – nominative plural (subject)
- Reason: subject of the verb förum
á lítið sveitasafn
- lítið sveitasafn – accusative singular (neuter)
- Reason: á
  - movement “to” a place → accusative
nálægt borginni
- borginni – dative singular, definite form of borg
- Reason: nálægt governs dative

So the main pattern:

dative after á (for time) and after nálægt
nominative for the subject við
accusative for the destination lítið sveitasafn