Transportion:

Communication

Shopping

Sights

Food & drink

Tours:

Weather

Hospitals:

History-About:

The first permanent settlement in Iceland by Norsemen is believed to have been established in Reykjavík by Ingólfur Arnarson around AD 870.
Steam from hot springs in the region is said to have inspired Reykjavík's name, which loosely translates to Smoke Cove.

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Source: Reykjavik City Guide

Hospitals:
Landspítali Hospital 543 1000 Norðurmýri, 101

National University Hospital +354 5 560 10 00
Address:  	Landsspitalinn, V/Eirikisgata
 
Reykjavik City Hospital +354 5 525 10 00
Address:  	Fossvogi
 
 Reykjavik Primary Care Center +354 5 585 13 00
Address:  	Heilsuverndarstoo Reykjavikur
Baronsstigur 47

Transportion:
Bus map | Strætó.is
Hop On - Hop Off Reykjavik Excursions (www.re.is)

Keflavik International Airport is on the Reykjanes Peninsula South West of Reykjavik
Reykjavik: Public Transportation - TripAdvisor

Food & Drink:
GEYSIR Bistro (www.geysirbistrobar.is), 2 Adalstraeti
Classic seafood: Vio Tjornina (www.vidtjornina.is)
Splurge: Sjavarkjallarinn (www.sjavarkjallarinn.is), or "Seafood Cellar
Hot dogs: A simple stand near the harbor called Baejarins Veztu Pylsur (literally means "best hot dog in town,"
Reykjavik Restaurants: See 201 restaurants with 6,604 reviews - TripAdvisor

Communication:
Most restaurants have Wi-Fi
Cruise Liner Visitor Centre http://www.whatsinport.com/Reykjavik.htm offers computers and is a Wi-Fi hot spot.
The Harpa - Reykjavík concert hall and conference centre has free Wi-Fi
Top Shop (Laekjargata 2A, near the city lake) - Internet Cafe
City Library Branches.

Links:
Kolaportið Flea Market on weekends in Reykjavík, Iceland - Lonely Planet
See Iceland for local tours Geyser, Blue Lagoon, ...
Brochures and Maps - VisitReykjavik
Reykjavik at CruiseCritic.com