Reykjavík cruise port car rental.

First thing is you need to know which cruise port you are using at Reykjavík-Miðbakki Terminal (the Old Harbour, in the City Centre),
Kornagarður Terminal – Sundahöfn (about three miles out of the city). or Skarfabakki Terminal Sundahöfn (about two miles out).

From the latter two I'm pretty sure there is nothing car rental wise within walking distance (such as under about an hour). It would be taxi to the rental lot- and going to the domestic (city) airport may well be as easy as anything else. Maybe they will deliver to the port?

If at the old harbour then yes there seem to be city centre places to rent from. The ship will run a shuttle bus into the city centre- at a cost.

I'm guessing you are on the Celebrity Eclipse, which is far too large for the Old Harbour- so you are at one of the out of town docks.

Thanks! Starting to think we'll just take a Viator of the Golden Circle.

Looking at Google Maps, Kornagarður Terminal is one spot among a group of adjacent cruise terminals, where our Windstar 7-day circle cruise started from. It's a very industrial area, with sections that can be hard to walk between, because of security fencing. Our return was to the more central Miðbakki Terminal.

It greatly restricts your choice of rental companies to select one that has branches anywhere other than the airport. But I chose Avis because they had a second office at Holtagard 104, open only 8AM-2PM!!! It was a small strip mall on the top deck of a multi-story parking garage. This was a one mile walk to the cruise terminal we were assigned to. So I dropped my wife and the luggage, and returned the car alone. It was a very long one mile walk. (Note that one half of a couple is not allowed to check in or deposit luggage for a cruise ... ... ... ) The walk did mostly have sidewalks or low-traffic roadways.

We had the car for four days of driving, upon air arrival in Iceland. We returned the car on Embarcation day, and took a "Ship Excursion" on Disembarcation that included a city tour and delivery to the airport in time for our flight. (With 50 other people on a bus.) This was the worst "ship excursion" I have ever been on in ten cruises. We should have used a taxi to the airport.

Changing the subject, I support your idea for a package tour because distances are so great in Iceland, and you have much more assurance of "accomplishing" the general concept you hope for with someone else doing the driving and the arrangements. I would also point out that this is, in Iceland, a very common decision for all kinds of people. It is NOT a dusty service for old people or fearful travelers who want three separate "sights" delivered to them, with 35 minutes free time at each place. (Not slamming, we've done this in Lisbon and in Madrid.) Rather, it is a common solution for families, young people, and mature travelers.

The other issue is the crowding and poor condition of many parking lots, the need for five kinds of car insurance, and narrow roads. You do not need 4WD in the summer, but high ground clearance is advisable.

Edit: typos

If you take a taxi to the wharf area there is a Blue Car Rental office there.

If you do a tour, which is a great option, book directly with the operator vs Viator. Troll.is is excellent and we have used them for various guided excursions.