You can stroll from one end of downtown Reykjavík to the other in about half an hour. But you shouldn’t. Instead, take time to weave in and out of side streets off the main drag, Laugavegur, which morphs into Bankastraeti, which then becomes Austurstraeti, as you head into the heart of downtown. The residential neighbourhoods are home to some of the most uniquely Icelandic sights of the city: brightly painted, corrugated iron homes, murals, lava rock gardens, corner bakeries, tucked-away cafés that turn into loud pubs at night, and some remarkably friendly cats. Klappastigur, quickly developing into the Shoreditch of Reykjavík, is one small street that is well worth a stroll. Stop at Sírkus (see below), a great little bar with an outdoor patio in the summer.

Another unusual way to tour the city is by pool. Because of the abundance of geothermally heated water in Iceland, nearly every town in the country and every neighbourhood in the capital has its own small pool, each with a distinct character. Sundhöllin (Barónsstígur, 551 4059), the oldest indoor pool in Reykjavík, is graced with vaulted ceilings, old-fashioned locker rooms and a balcony hot tub frequented by good-natured locals. Or, if you want to go high-tech, head for Laugardalslaug (Sundlaugavegur, 553 4039), a swimming pool complex complete with outdoor and indoor Olympic-size pools, steam baths, waterslides and five or so hot tubs of varying temperatures. A hyper-modern gym is attached.

• Tourist information: Adalstræti 2 (590 1500, www.tourist.reykjavik.is).