Travel from cruise port to Reykjavik

"Best" is a subjective term.

First you need to know where you are docking.

Big cruise ships dock at Sundahöfn (which is close to 3 miles from the City Centre.

Medium sized or small ships dock at the Old Harbour, opposite the Maritime Museum- within walking distance of the City Centre.

There are always taxis at Sundahöfn and the HoHo bus calls at the Terminal, scheduled as every 30 minutes on days when ships are in.

Most lines also provide a Shuttle Bus, which is normally more expensive than the HoHo bus.

It is a nice if lengthy 45 minute walk (done it) along the sea front to the Harpa Concert Hall- a very useful place for free restrooms

Finally there are citybuses routes 12 and 16 which stop on the main road just outside the terminal- https://www.straeto.is/en

There is a 24 hour ticket you can buy or a City Pass- buses + admissions to Museums and the various Thermal Pools in the City- https://visitreykjavik.is/reykjavik-city-card

So lots of choices.

EDIT- You will almost certainly have to take a shuttle bus from the ship's gangway to the Terminal Building, where you change onto whatever transport you are taking into the City.

As it happened, our Windstar cruise left from the more distant cruise port, and returned us to the more downtown one. I think we took the cruise's Airport Transfer with Reykajavik Tour product, which was not very satisfactory. We got to the airport in time, although the security line was so long they had to turn off the escalators. We avoided handling our luggage, but it was Sunday, so the Cathedral was almost inaccessible, and the tour stops were banal and forgettable.

I chose my car rental company partly because they had an office within walking distance of the distant cruise port, where we embarked. Most of the "local" and "bargain" car rental companies seem to have only one office.