Learn Icelandic: Hvaða staður er opinn núna?

No, and that is great news! Unlike many other Icelandic words, the question word hvaða (which/what) is completely invariable. It always stays exactly the same no matter the gender, number, or case of the noun that follows it.

Why does the adjective end in "-inn" here (opinn)?

In Icelandic, adjectives must match the gender of the noun they describe. Because staður (place) is a masculine noun, the adjective for "open" must be in its masculine form, opinn. If you were asking about a neuter noun like hús (house), it would be opið.

Why is the verb er placed after hvaða staður instead of right after hvaða?

In Icelandic questions, the verb usually takes the second position. Here, the question word hvaða and the noun it attaches to (staður) stick together to form a single unit. That entire phrase acts as the first block of information, so the verb er takes the second slot right after it.

What is the difference between núna and just saying nú?

Both words mean "now" and are often used interchangeably. However, núna usually puts a bit more emphasis on "right at this exact moment" compared to nú, which is perfect for this sentence where someone is actively and urgently looking for a place that is open.