One of the best parts of living in London is the opportunity to travel around Europe - the city is a hub for cheap flights and between Fall or Spring Break, long weekends with friends and travel after the semester is over, you'll be sure to leave NYU London as a seasoned traveller - just don't miss out on everything the UK has to offer as well!
It is a good idea to have an idea of the sites you want to visit, as well as things you want to do during your trip. Do some research on travel blogs and communities. You should ask friends and family who have traveled before about places they enjoyed the most. Read through site-specific guide books like Lonely Planet, Let's Go, Rough Guide, Rick Steves, or Frommers.
Although you will want to book all travel as far in advance as possible, you should not book any trips until after the first week of classes, as you may find that there are already NYU sponsored trips in place.
If you are planning weekend travel, then flying from city to city may be your best option - you'll be surprised at how cheap compared to some domestic US flights. Try Skyscanner to find the best deals.
Heathrow Airpot is easily accessible from the NYU London residences, but many of the cheapest flights leave very early in the morning and from airports outside of the city. It can be difficult and expensive to travel to these airports at these very early times because public transportation may not run all night, but there are some buses - ask in the Student Affairs Office if you need help arranging this.
This site is specifically for train travel within the United Kingdom.
This train will take you from London St. Pancras station into Paris and beyond into the heart of Europe.
If you are planning on traveling (especially after your semester) you may find that Eurail is the best option. It is a train pass that gives you train travel within 28 European Countries. Not only is it a cheap, convenient way to travel around Europe, but also many Euro trains are super comfy! Buy your tickets in the US as they are more expensive in Europe.
This site is specifically for bus travel within London, United Kingdom. Here you can plan trips and see bus routes and maps.
With Megabus, you can travel throughout the UK for as little as £1.50. Megabus also tickets for overnight coach journeys to several cities in Europe, which can be a cheap alternative to flying.
Busabout is designed for back-packers which makes it a great way to meet people, and a cheap way to get around—it may be more appropriate if you plan to do more traveling during the summer.