With a population of around 123,000, Reykjavik may be the smallest capital city you'll ever visit. Think Gloucester or Slough in England for population level. It has the amenities of a big city, but you can walk across it in less than an hour, passing colorful houses and shops in historic buildings

Reykjavik is the commercial and government center, so you can rub shoulders with people who live here if you pick the right spots. Start off your Reykjavik city break seeing the main sites after breakfast. Then check out the locals' side of the city in the dark—if it's winter—or in unending daylight if you arrive in the summer.

Morning: 9 a.m. – 12 p.m.

To kick things off, indulge in two of the city's specialties: fine coffee and bakery treats. Some of the best atmospheric options for getting both are Sandholt Bakery, Stofun Café, or Café Babalu, but there's seemingly at least one coffee shop on every block. For something hearty to last through lunch, grab a big meal at Laundromat Café.

To get your bearings and some background, connect with a CityWalk “pay what you want” walking tour or get a less standard itinerary with I Heart Reykjavik for 5,500 ISK (£40). Armed with a new sense of direction, you can return later to any of the sites you missed.

Afternoon: 12 p.m. – 5 p.m.

You can navigate much of this city on foot, so it's easy to peruse menus as you pass by. The best budget option in this expensive city is at Bæjarins Beztu Pylsur—translation “the best hot dog in town.” It's made with local lamb and two kinds of onions. Otherwise, the coffee shops' lunch menus usually switch to sandwiches, soups, and salads in mid-day.

Make an excursion to natural hot springs or swim in an outdoor heated pool in the afternoon (see the “Trip Tips”) or get intentionally lost in the neighbourhoods to get a feel for the Reykjavik street art scene. For some education, visit a museum about Iceland's history, see The Settlement Exhibition, tour the Viking Museum, or gawk at certain protuberances in the Icelandic Phallological Museum. Visit Iceland's highest church Hallgrimskirkja for the obligatory panoramic photo, or head to the top floor of the Harpa Concert Hall instead for a less Instagrammed shot through the geometric windows.

You'll want to take advantage of happy hours in Iceland if you're up for a couple drinks. Drink specials start as early as noon here and 3:00 p.m. is common. Try cozy Kaffibarinn or Bravó to avoid the hostel bars filled with other travelers. Feel in the know by grabbing a draft at the extension of Denmark's craft beer chain Mikkeller & Friends.

Evening: 5 p.m. – 12 a.m.

Summer days never end here, but if it's a month with a sunset then swing by the Harpa Concert Hall to see the artistic building design meant to simulate the Northern Lights. Stroll around the old harbour to watch the boats and mountains glow orange.

If you've got the budget for a Scandinavian splurge, have dinner at highly regarded Matarkjallarinn, Michelin-starred Dill, or 3 Frakkar for adventurous local fare. For a meal that won't require two days' wages, grab pizza at Devito's or choose from different vendors at Hlemmur Food Hall.

Reykavik has a lively music scene and your best chance of catching the next Bjork or Sigur Ros may be at two side-by-side music venues: Húrra and Gaukurinn. What happens after that? That may depend on whether you can extend your flight…

Trip Tips

You've got plenty of choices for outdoor soaking here since hot water is bubbling up to the surface island-wide. The famous choice is the Blue Lagoon, but it will take you the better part of an afternoon to make the costly excursion. Some travelers schedule this before a flight out since it's out past the airport and has bus connections.

With a rental car you can go further to the Secret Lagoon and see more of the countryside. If time is short though, it may be best to join the locals. Visit an outdoor swimming pool in town that's naturally heated such as Sundholl Reykjavikur public baths or giant Laugardalslaug.

For transportation to and from the airport, the top choice is frequent Flybus, which was around £18 to£22 each way, at the time of writing.