What are the most worthwhile things to do in Reykjavík on a first visit?

That designation rests on a genuinely unusual set of numbers. The city holds the medieval Icelandic manuscripts, including the Sagas of Icelanders and the Eddaic poems; the Árni Magnússon Manuscript Collection was added to UNESCO's Memory of the World Register in 2009. Iceland publishes roughly five titles per 1,000 residents, against two to two and a half in the other Nordic countries. Halldór Laxness won the Nobel Prize in Literature in 1955. The Reykjavík International Literary Festival has run biennially since 1985, and an International Children's Literature Festival biennially since 2001. The Reykjavík City Library is the country's largest public library. Cities in the Creative Cities Network must submit a progress report every four years to keep the title, so this is a maintained status rather than a one-off award.

The National Museum of Iceland is the single best indoor use of a day. It opens daily from 10:00 to 17:00, with admission at 2,500 ISK for adults, 1,200 ISK for seniors and students, and free entry for children up to 18. From October to May it runs a free family tour on the first Sunday of each month at 14:00, though adults still pay the 2,500 ISK admission to join it.

Hallgrímskirkja's tower is the cheapest viewpoint in the city at 1,400 ISK for an adult and 200 ISK for children aged 7 to 16 — but it works around the church's own life. The tower closes from 10:30 to 12:15 on Sundays for the 11:00 service, and it shuts during the 12:00 organ concert on the first Saturday of each month from September to June. It stays open through the Wednesday and Thursday morning services and the Thursday meditation and organ music.

Then there are the pools, which are a civic institution rather than a tourist activity. Laugardalslaug, run by the City of Reykjavík, is built around a 50-meter pool with both outdoor and indoor water, hot tubs, a cold tub, a whirlpool bath, a salt water tub, a slide, a children's slide and a steam room. It opens 06:30 to 22:00 Monday to Friday and 08:00 to 22:00 at weekends.

Laugardalslaug's 50-meter pool is outdoors and geothermally heated, so swimmers are in warm water with cold air above it — the steam coming off the surface is the thing you notice before the swimming.

The free family tour at the National Museum is free for the children, not for the adults bringing them — the 2,500 ISK adult admission still applies, and the tour runs only on the first Sunday of the month between October and May. Families who read "free" and plan a June visit around it find neither the tour nor the discount.

• Morning — The pools open at 06:30 on weekdays, hours before any museum, which makes them the natural first stop on a short day.
• Midday — Avoid the tower between 10:30 and 12:15 on a Sunday; that window belongs to the 11:00 service.
• Afternoon — The National Museum runs to 17:00 daily, and at 1,200 ISK for students it is the best-value indoor hour in the city.

Almost every opening time here is conditional on something else. The tower's Sunday closure, the first-Saturday organ concert from September to June, and the last-Thursday-of-the-month evening service all suspend access without being obvious from a ticket page. Icelandic prices are high in absolute terms — 2,500 ISK for one adult museum entry adds up fast across a family — and the Creative Cities title's four-yearly reporting requirement means designations should be checked rather than assumed when a page is a few years old.

For what to eat between the pool and the museum, see the Reykjavík food and drink question in this group.