Make sure you have a nice pair of comfortable shoes for the trip. This is the utmost important to have a good time. I highly recommend bringing shoes that are broken in. It will only take a few hours to get a foot blister and many days of irritation.
Bring with you at least one credit card (and one for backup). If you have enough time before the trip, you can apply for a credit card with little or no transaction fees. Here is one website which lists the credit cards and their fees http://www.flyerguide.com/wiki/index.php/Credit/Debit/ATM_Cards_and_Foreign_Exchange.
Also bring your ATM card. Again check with your bank for the foreign transaction fees. Expect to pay between 1%~3% per transaction.
Don't forget to call your credit card company and your bank to tell them that you'll be traveling oversea so your transactions will not be rejected.
Get travel books. If you are traveling there for just 1~2 weeks, the Top 10 books on London, Paris, and Rome are ideal. They contain a lot of useful information for each of the top 10 things you need to see. They also make suggestions on what to eat, where to live, and what to watch out for. Each book has foldout maps of the city, as well as metro line maps.
Book hotels ahead of time. This is a more assure way to get a cheaper deal as well as a peace of mind. Try different websites such as priceline.com, cheaphotels.com, venere.com. One thing to note here, try to get hotels close to where you will be spending most of your time (i.e. central city). This way, one can still hangout at night without worrying about getting to your hotel by metro at late hours (in a strange country). Also, one can take breaks in the middle of the day as well. Yes, it will cost a bit more, but if you book ahead of time, it's really not that bad.
There are a couple of ways to get from London to Paris. However I think the de-facto way is to take the express train Eurostar. It takes you directly from central London to central Paris in 2 hours and 15 minutes.
To get from Paris to Rome, I would suggest to take http://www.easyjet.com/ or http://www.ryanair.com/site/EN/. It's cheap and in my opinion the best way to go.
What to Pack - pack light
1. passport/visa - US citizens do not need a visa to England, Italy, or France as long as the duration of stay is within 30 days
2. necessary wardrobe - you will need COMFORTABLE walking shoes.
3. necessary Toiletries
4. Camera
5. Credit card / bank card - do not bring too much cash with you incase of pick pocket - they have ATM everywhere in the cities for you to withdraw money. just check with your creditcard company and banks to activate forgein with daws - also check the rate (some credit card charges 1% on each withdraw whereas others charge 3%).
Food that I love:
England - Try Chicken pasty at the covert Garden, smosa at any indian snacky places
Paris - any Paninis at street vendors
Rome - pocket Kebab (turkish)! Pizza and pasta are okay...
