I don't think wisdom has much to do with it, except in deciding not to travel to war zones or where there is a danger of being kidnapped. Where to go should be probably decided by your interests. If you studied a foreign language, a country where that language is spoken would be a natural choice. You are going to travel alone, perhaps? Then try getting some sort of pass, cross the channel, and let whim be your guide. Most young americans (are Brits much different?), just out of university, tend to go to europe and just explore wherever fancy takes them.
New York will blow your mind. Italy might be great for someone from the UK, but get out into the countryside, or go to Sicily or Sardinia so you get a cultural change and run into fewer Brits and Americans. I think Scandinavia is great, but you might feel it is too similar to your home country. It really depends on if you are traveling for adventure or for relaxation. Judging by your youth, I would imagine it is more for adventure. Switzerland and Austria are fantastic for rock climbing and hiking. A nice quiet Italian beach town like Céfalu (Sicily) is a great come down after some ruin climbing in Agrigento. Travel is a great education. Enjoy!
Well Ireland would be a very easy first place to go, no culture shock at all. My first foreign trip (I waited way too long) was Belgium and I loved it straight away. You can go on the Eurostar so no messing around with airports and the station is right in the middle of the city. France and Holland are good for the same reason.
A good decision to make early on is: am I a city, beach or walking in the country person? This will really help to narrow down where to go.
If you can afford it and someone will go with you the best place that I have loved so far has been Hawaii in all it's beauty from the water to the people there. The shows are great and the beach is to die for. Been to 2 islands so far and hope to go back in a few years and hit another one.
If you want a summer gay beach vacation, there are always Ibiza and Sitges (near Barcelona). Very gay, lots of foreigners, so there will be some english spoken, and (for Barcelona) lots of culture as well on days off from the beach. Spanish is probably the easiest language for an english speaker to learn, so you could easily pick up a few phrases for those rare occasions when english is not spoken. Like, Tus ojos son hermosos. Quiero chupar.