Reykjavík's historic City Center of museums, historic sites, restaurants, and shopping, emanates out from the harbor.
If you want to stay over in Reykjavík, book a hotel in or near City Center. The Hilton Nordica is a convention hotel for business travelers and meetings. Just nearby is Bolholt Apartments, a self-service hotel for budget travelers. Both are located near the top "40" marker in the map above. If you want to stay inexpensively in the City Center, consider the Loft Hostel. (To find hostels all around Iceland, click here.) There are many more hotels in City Center, which you can book through Hotels.com, Expedia, Orbit, etc.
When you get into town, purchase a City Card. It gives you access to the public busses and entrance to historic buildings and museums. City Card also gets you discounts at select tour companies and restaurants. Go to VisitReykjavik.is to learn more about the benefits. You can buy a City Card at the Hilton, other hotels, and tour offices.
TRANSPORATION AND TOUR COMPANIES
Iceland On Your Own (self-service)
Reykjavík Excursions (self-service)
South Iceland Adventure (custom group tours)
VisitReykjavik.is (City Card tourist discount pass)
Flybus (airport shuttle)
When we visited with a convention in 2014, Iceland Travel arranged our stay in Reykjavík, and South Iceland Adventures took us on a four day trek to Thórsmörk National Park. This map shows the route from Keflavik International Airport to Reykjavík, then south to a retreat center in the south. Click here for my south shore photos.
Most of the population lives around Reykjavík, so there's a lot of wilderness. All of the tour companies listed above will get you passage to nature, or to go out on the water. The paved roads are great, so you can rent a car and go on your own. However, if you plan to go off-roading like we did, be sure to go with competent guides. The guides from different companies work together to make the tours as safe as possible in the extreme conditions of the Icelandic wilderness. Check out the links above, to find the right option for you.
If you only have an eight hour layover in Reykjavík, consider a day at the Blue Lagoon. It's an outdoor lagoon where you can bathe in natural, thermal sea water. They have spa treatments, hiking trails, restaurants, and an observation deck. Link to BlueLagoon.com for details. General admission is $10; entering the lagoon is extra, and best booked in advance to assure availability.