It really shouldn't come as much of a surprise that countries that rely heavily on tourism for their income are some of the first to come to the table as far as relaxing, or in some cases completely eliminating, Covid restrictions for entry.
Cyprus is a bit more expensive than most of the kind of places that I would normally travel to, but as of March 1st, you can freely enter if you are double vaccinated.
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If you are unvaccinated and from the United States you can enter Cyprus with a negative PCR test taken within 72 hours of arrival. There might be other countries that can also gain entry without vaccination, but I can't find information on that for certain, sorry. You can check your country of origin to see if unvaccinated from your country can enter by going here
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Like a lot of famous travel destinations in the world, Cyprus is mostly known for its wonderful beaches and crystal clear water. I have been to Cyprus many years ago and I didn't stick around for very long because as budget-travel is concerned, I don't really think that Cyprus is one of them. However, prices have been dropped dramatically over the past 2 years due to the supply of accommodation far exceeding the demand. If you have experience in traveling around Europe, Cyprus is cheaper than most of Western Europe, but more expensive than other nearby Eastern European countries. When I was there a while ago, it was quite difficult to get any accommodation for less than $50 a night, which for most backpackers is going to be a lot more than they want to spend. The only budget places that I was able to find were in the cities of Nicosia or Paphos.
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Paphos is where I spent most of my time because while it is still a large-ish city, it is on the coast whereas Nicosia is a giant sprawling city that while not as crazy as other capitols, kind of lacks the charm of nature that I think most travelers would like to see while abroad.
I wouldn't recommend going JUST to Cyprus for any budget traveler because generally speaking I do not consider this to be a budget destination at all. When I was moving around Eastern Europe, Cyprus was one of the most expensive places I stayed the entire time I was there. For beaches that are very similar and a lot cheaper head to Albania or Croatia instead.
It is worth noting that the prices of accommodation in Cyprus are at a 20 year low right now though and this window is quickly closing as most of Europe seems to be in a race of sorts to see who can remove the Covid restrictions the most in order to attract the most visitors. This could be a unique moment in time as far as values are concerned in Cyprus, which is a place I normally consider to be out of my price range.
The main point of writing this was to indicate that there are basically zero restrictions in Cyprus as of March 1st, 2022. If you ask me, it is about time they did this and I am happy to see this trend happening all around the world.