Keflavík International Airport: Take a scheduled airport coach (Flybus/Reykjavík Excursions or Gray Line) to the Reykjavík terminal, then add the hotel drop-off only if your accommodation is genuinely awkward for Hlemmur/BSÍ. Expect roughly 45–60 minutes to central Reykjavík and about 4,000–5,000 kr one way. There is no airport train. A taxi is convenient only for a group or a very late arrival; it is dramatically more expensive.
Reykjavík Airport: This is the domestic/Greenland/Faroe airport beside the centre, not the international airport. Downtown is a short taxi ride or a manageable walk in decent weather with light luggage; use a local Strætó bus if its routing suits your hotel. Do not mistakenly book ground transport to KEF: the two airports are about 50 km apart.
Sundahöfn cruise harbour: Cruise ships commonly use Sundahöfn, around 3 km east of the centre. Use the ship shuttle if included; otherwise take a taxi or a bus rather than assuming the old harbour sights are walkable with a tight port call.