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This is one of those things that's really up to you. A day's car rental is probably about the same price as a Golden Circle bus tour for two adults, so it comes down to your personal preferences.Renting your own vehicle means you can set your own pace and schedule, linger at attractions you particularly enjoy, have some sites all to yourself between tour bus arrivals, and avoid waiting for the one slow couple that always takes their time getting back to the bus.
Taking an organized tour means you don't have to plan your route, worry about driving in winter weather, or risk running out of daylight; both of you can also (if you wish) take a nap between stops.
Self-driving gives you the option of going out looking for northern lights on your own, as well. (Find someplace with mostly-clear skies, no lights, and a relatively unobstructed northern horizon.)
