I will be in Iceland for three nights during the new year holidays.The are different websites that offer tours in Iceland with different prices. I can also take bus or rent car and explore by myself. I am wondering which option is more economical, safe, and carefree?
As you only have limited time and it is likely a busy time in winter, I think prebooking tours at this time of year makes sense. But when I was there in September, a few years back, I waited till I was there and could book in one of the many offices.
Whether regular buses or a rental car is suitable for you is more a matter of opinion and I do not answer that kind of question (nor do I have the needed knowledge) but you need to consider that if the weather turns real bad with you stranded in your car or without buses it it goes really bad. So before you set out, check the weather forecast. If booking tours, the tour companies will do that for you.
Economical and carefree option is usually when you travel by yourself.
There is lots to see there in many places. You want to see all the major Waterfalls, do the Glacier walk, go hiking up some of the well marked hiking trails. do the boat ride on Lake Jakulsarlon ( home to 2 James Bond Movies).
But taking tours to all those places might be quite expensive.
Still, since you are going in Dec-Jan it might not be safe to drive a car around the island, if you aren't comfortable with driving on snowy roads. And bus schedule may change according to weather conditions.
Of course you can check the weather forecast beforehand. But if you're really concerned about safety, better to take a tour.
Car vs. organised tour on your three categories.
Economical: we can’t answer that. It depends which specific trips you’re planning and what kind of car you’d rent, among other things. If you gave us enough information to figure this out, you’d already know the answer yourself.
Safe: also somewhat dependent on what you’re doing. In many cases being part of an organised tour might offer a little extra security, but if you’re going to travel alone there probably aren’t all that many places safer than Iceland from a personal security perspective. Obviously, if you’re intending to go exploring the (mostly uninhabited) central regions, go mountain climbing, etc, that can tip the safety balance much further towards organised tours - unless you have experience you shouldn’t attempt those activities without guides. But that’s because those activities carry inherent dangers, not because travelling alone is particularly dangerous in itself. As you’re travelling in winter, you should consider the weather. Icelandic winters aren’t as cold as many think, but nevertheless you should certainly expect snow. High winds and fog are also common and can arrive quite suddenly (a saying I’ve heard regularly when visiting Iceland: “if you don’t like the weather, wait 5 minutes”) . If you don’t have experience driving in such conditions, that’s certainly something to think about and may be a good reason to avoid driving yourself.
Carefree: If you take organised tours you have to work to their schedule. If you drive yourself you can go more or less where you want when you want (opening hours permitting, but many Icelandic attractions are natural sites open 24hrs a day - although during winter that doesn’t necessarily mean you can see them for more than a few hours even if you can go there). Of course, driving yourself also means you are responsible for planning a realistic timetable to get everywhere you want to go (and back, if applicable). For me, the car is the obvious winner here, but that may be different if you find that kind of planning particularly stressful. The points above about the weather are also relevant here - tours should ensure you don’t find yourself stuck in bad weather without necessary supplies/equipment, if you go by yourself that’s on you. Don’t let this out you off too much: common sense while planning should be enough, just as long as you’re aware of the possibilities.