Thanks all. When I say cheap I mean staying in backpacker hostels, limiting drnking money to a couple of night a weeks and food to a standard 3 maybe 4 meals a day (gonna skin and bones by the end of it). It's something I've wanted to do for a while so going to get 2 jobs untl Christmas to save. I'm budgeting about £6000 for 4 months including a round the world ticket.
Definitely thinking NY now...vegas will probably be a bit pricey with all the money I'll lose gambling.
This seems as if it will be a vacation to remember for sure. I myself would love to see the world -- though via smaller trips and not as cheap.
As for your original question of choosing between New York City or Los Angeles...
Speaking as someone who has lived in both cities, it's rather like comparing apples and oranges, as the two are so different from each other. I'm not saying that one is, overall, "better" than the other. Both have good things to offer their visitors and both have their drawbacks. They're both fascinating in their own ways. Some people prefer NYC for the reasons touched on above, but some (especially Europeans and others from older cities) prefer LA because it's so different from older cities. Each city really needs to be considered on its own terms and it really depends on what you're looking for. Plus, there are some things to consider.
It looks as if you're starting your trip in the middle of what would be the winter season here in the US. Do you mind exploring a city that may very well be under snow (I love New York, but sometimes the getting around in the snow can be a pain) or would you prefer a city where winter means temperatures in the very pleasant 70s (F) and little more extreme than some rain (that's basically LA in February)?
If you plan to drive from LA to Las Vegas I would also plan on spending at least a night in Vegas (not just a daytrip where you would drive there and back in one day); the drive takes too long for a daytrip. It's not something that can be done in just a couple hours, like driving, say, from New York to Philadelphia.
New York is, of course, one of the cultural capitals of the world and has more cultural venues than any other US city. LA, however, has many cultural venues that are very well regarded, too, so I definitely wouldn't discount LA based on that alone.
Another thing to consider is how to move around within either city. Public transportation in New York (especially Manhattan where you would spend most of your time) is cheap and relatively efficient using the subway. New York is also oriented toward pedestrians and getting around on foot is not only a wonderful way to experience the city, but in many instances, may very well be the most practical way. Manhattan's buses are generally slow, but cheap, clean and good for going short distances that are too long to walk (if that makes sense). An occasional, brief cab ride in Manhattan shouldn't bust your budget either.
Unlike New York, which basically has one huge, principal commercial "center" (Manhattan), Los Angeles is made up more of a patchwork quilt of smaller "centers" or districts, each with its own character and features (e.g., Downtown, Hollywood, Westwood, Venice, Santa Monica, Beverly Hills, West Hollywood, the Sunset Strip, etc.) often with some suburban-style distance between each. If you're limiting yourself to just one of these these smaller, relatively compact areas, walking could actually be relatively practical. However, to move from one such area to another and to otherwise move about practically and efficiently you would really need to drive a car (a rental, I would assume), with its attendant costs (rental fees, insurance, fuel and parking) or use one of the various taxicab services in LA (though hiring one is not as convenient as in NY and they tend to be more expensive because the distances tend to be much larger in sprawling LA than in compact NY). LA does have a very nice subway/train system but it serves a relatively limited area in the downtown area (it does extend through the center of Hollywood, though). LA's buses are almost as slow a NY's and are not recommended to travel long distances (though they can be good within the limits of individual districts of the city).
You can eat as cheaply or as expensively as you want in either city and both have cuisine from all over the world. It's a bit easier, I think, to find cuisine from anywhere in the world in New York (though it's never as good as it would be in the original country, of course), partly because you can take a stroll within many areas and happen upon such places. In any case, the food carts on the street are a cheap option, though they really do overcharge for what they provide (and I always wonder where the food comes from). A better option are the many delis and smaller, casual, cheap (indoor) restaurants and eateries to be found in virtually every neighborhood. Also, there are pizzerias everywhere (though, of course, they're not necessarily good for your figure -- just avoid the ones that overcharge; $8 for one slice of pizza is a ripoff).
There are cheap places in LA too, though you may have to hunt for them a little. Cafes and smaller eateries are an option. Pico Boulevard is supposed to be excellent for restaurants and non-American cuisine. There's always been an abundance of good and cheap Mexican cuisine in most LA neighborhoods, which is good if you like that type of food. You may also appreciate that LA, always conscious of appearances, has more health-food options than NYC does.
And both cities have plenty of cheap Chinese restaurants everywhere.
I'd like to have a better idea of what sorts of activities you would like to do. Are you going to stay mainly in cities? Or, do you also plan to see some natural wonders?
There are areas of natural beauty near both cities. Outside New York, parts of the Long Island shore are quite lovely, as is the New Jersey shore. If you have time to go to upstate New York, Niagra Falls is definitely worth a visit. On the other hand well-known beaches (Venice, Santa Monica, Malibu) and the Pacific shore line one edge of Los Angeles, which is otherwise ringed by picturesque hills, mountains and canyons with the desert not so very far away.
One more thing: It looks as if you're going to be spending a lot of time in Australia, Southeast Asia and other areas around the Pacific. In terms of airlines and travel, Los Angeles is the largest gateway between the US and points west in the Pacific and seems to be used more often than other US cities by transPacific travelers. I don't know where you're flying into the US from, but if you're going from the US directly to a destination located on or near the Pacific, it's quite possible your itinerary would include a stop at the Los Angeles International Airport (LAX) anyway, even if you choose New York.
Well, whatever city you choose, it'll be a memorable stop.
If you have any concerns about either city feel free to pm me.