Over this summer, I will be going to Europe to attend a pair of mathematics conferences. Because they are close together, I'm planning to spend the intervening time (most of the month of July) in Europe.
It is my first time going to Europe. I am very excited. I am certain that I will have fun.
I am equally certain that I will have more fun if I consciously attempt to maximize the amount of fun I will have.
However I know absolutely nothing about Europe; I have never been, I have few if any friends or family there.
So my question is, what should I do in order to have the best possible time in Europe?
I appreciate information that is useful for me specifically, as an American graduate student who has never been to Europe, who will be in Rome in early July and need to be in Barcelona by the end of July; the best ways to get around, benefits to being a student, events happening in July, visas that I might need. I intend to look for Less Wrong meetups occurring during my stay.
I would also appreciate general Europe information, such as excellent sight-seeing locations, the best way to buy food (I hear buying groceries in France is cheap and restaurants are very expensive), how difficult it is to move between different countries, the advantage to staying in one place for some time versus taking more of a tour of the continent.
There are certain types of information that I am not particularly interested in, but that I think would be appropriate to discuss in the same context. For example, what is the best way to find the cheapest flights or choose when to go on vacation (my flights are reimbursed and my timing is determined); what would make Europe an ideal vacation location, as opposed to Australia, Asia, South America, etc.
If people are interested in more details of my specific situation, I am happy to give them in the comments or private messages.
Read wikitravel articles on every country you are interested in. Also read travelblogs and/or forums. There are surprisingly many people that make make backpacking a lifestyle. Decent preparedness is very helpful. You should also brush up on where the EURO is valid and what and where the Schengen-space for easy traveling in the EU is. If you never been outside of the US read some other traveling reports as well. US passports actually contain a manual on how to use a passport, figure out why. Some different habits are important to know upfront., e.g. legal ages for drinking, strange laws that forbid stuff you are used too, and the other way round. Countries where Credit cards are not generally accepted, how to be polite in a way that the locals can deal with. Europe now also has cheap air-flight. Watch out for easyjet, ryanair, airBerlin, and many other lowcost carriers. Train travel also actually works for all of Europe, as do buses (Eurolines). My preferred mode is to pre-plan all the trips, with decent buffers for mishaps.