Start at Hallgrímskirkja in Skólavörðuholt, the easiest “welcome to Reykjavík” stop and the best way to orient yourself fast. If you can, go in the soft evening light — the tower is usually open into the evening in summer, and the view from the top gives you the whole compact city, the sea, and the mountains in one sweep. Expect about ISK 1,000–1,500 for the tower, and about 45–60 minutes total if you’re taking photos and soaking it in. From here, it’s an easy downhill walk into the center, so you don’t need transit yet; just follow the slope toward Laugavegur.
Stroll down Laugavegur for a low-key first taste of the city: design shops, wool goods, little cafés, and that breezy Reykjavík mix of locals running errands and visitors drifting between boutiques. Keep it unhurried — this street is better as a wander than a checklist. When you’re ready for a snack, swing by Bæjarins Beztu Pylsur near the downtown/Old Harbor edge for the famous Icelandic hot dog; it’s quick, cheap by Reykjavík standards, and a fun classic stop at roughly ISK 1,500–2,500 per person. From there, continue on foot toward Harpa, which is only about 10–15 minutes away and makes a great harbor-side transition before dinner.
At Harpa, take a slow lap around the glass façade and the waterfront — it’s especially pretty at dusk, when the building catches the light and the harbor feels calm and cinematic. Then head to Kol for dinner; it’s central, easy to reach from Harpa on foot in about 5 minutes, and a dependable choice for modern Icelandic-leaning plates, with a typical spend around ISK 6,000–12,000 per person depending on how much you order. After dinner, make your way to Sky Lagoon in Kópavogur by taxi or rideshare; allow around 15–20 minutes from downtown in normal traffic, and plan about 2 hours total for the soak, changing, and the full spa experience. Book ahead if you can, especially in summer evenings, and bring time to just sit in the water and watch the sky go pale — it’s the right final note for a one-day Reykjavík visit.