4h: With 4 hours around Stockholm (STO collectively refers to Arlanda ARN, Bromma BMA, and Skavsta NYO), you’re realistically limited to Arlanda or Bromma. From Arlanda, take the Arlanda Express (18 min) or commuter train (about 38 min) to Stockholm Central if you have at least 3 hours net. Focus on Gamla Stan: stroll the cobbled streets, see Stortorget square and the exterior of the Royal Palace, and walk along the waterfront towards Skeppsbron for city views. Grab a quick fika (coffee and pastry) at a café like Chokladkoppen or Kaffekoppen. Return to the airport at least 1.5–2 hours before departure (more for non‑Schengen or checked baggage). From Bromma, a taxi or Flygbussarna bus gets you into the city in about 20–30 minutes; you can do a short walk around City Hall’s waterfront courtyard and nearby Kungsholmen before heading back.
8h: With 8 hours, you can see several central highlights. From Arlanda, take the Arlanda Express to Stockholm Central. Start in Gamla Stan: explore the Royal Palace courtyard, the narrow alley Mårten Trotzigs Gränd, and the waterfront. Walk or ferry to Djurgården to visit the Vasa Museum (17th‑century warship) and, time permitting, Skansen open‑air museum for traditional Swedish houses and Nordic animals. Alternatively, visit Fotografiska in Södermalm for contemporary photography and city views from the café. Have lunch at a classic Swedish spot like Tradition (Gamla Stan) or Pelikan (Södermalm) for meatballs and husmanskost. Leave the city 2–2.5 hours before your next flight. From Bromma, similar plans are possible with slightly more flexibility; from Skavsta (NYO), the 80–90 minute bus each way to Stockholm makes a full city visit only worthwhile if your layover is truly 8+ hours gate‑to‑gate and you’re comfortable cutting it close.
24h: With 24 hours, you can experience both historic and modern Stockholm and even stay overnight in the city. After arriving (most likely at Arlanda), take the Arlanda Express or commuter train to Stockholm Central and check into a hotel near the station, Norrmalm, or Gamla Stan. Day 1: Explore Gamla Stan (Royal Palace, Storkyrkan, Stortorget), then walk to City Hall (Stadshuset) for a tower visit in season and views over Lake Mälaren. In the afternoon, head to Djurgården for the Vasa Museum and either Skansen or ABBA The Museum. Evening: dine in Södermalm at a traditional restaurant like Pelikan or a modern Nordic spot, then enjoy a drink around Mariatorget or Nytorget. Morning of Day 2: stroll Strandvägen and Östermalm, visit the Östermalms Saluhall food hall, or take a short archipelago boat tour if schedules allow. Plan to be back at the airport 2–3 hours before departure (longer for intercontinental flights), using either Arlanda Express, Flygbussarna, or commuter trains depending on your budget and timing.