Tez - My wife lived in NYC for 4 years and while she and I were living in New Jersey we spent about 1-2 weekends per month in NYC. So, we've stayed in the city MANY times. I'd be happy to help with anything you need.
In terms of reasonably priced Hotels, it really depends - as Terry said - what you consider to be reasonable. The last time that we stayed there, we paid about $120 per night. The hotel was nice and there were no problems with the neighborhood - but the rooms are TINY. But then, that's standard for just about any hotel in NYC under $300.
Stay FAR away from the bus system in NYC. If you live there, it can be navigated pretty easily, but for one time visitors, it isn't easy. The subway system is pretty easy though. I highly recommend something called NYC Unfolds. It is a pocket sized map that unfolds to show all of NYC including the subways, stops, and seriously EVERY tourist attraction you could ever want. It is made by vanDam, check out
www.vandam.com . Zagat's is also worth at least taking a look at, but its pricey and I wouldn't recommend a non resident actually buying one. Zagat's guide is basically a list of EVERYTHING to do.
As for stuff to NOT MISS:
The Metropolitan Museum of Art - "The Met" This is by far one of the greatest art museums in the country. Their collection is massive and the museum is amazing. There is a listed "price" to get in, but TRUST ME ON THIS ONE, because no one ever believes you. That is a donation suggestion, its in the fine print. Just give the lady a dollar and you'll get in. DO NOT PAY FULL PRICE AT THE MET.
The Rose Center/Museum of Natural History - Also a great museum, but the best part is that it is attached to the Rose Center, awesome planetarium....the building is incredible and the show is stunning. It is actually in Spiderman 2 if you've seen the movie.
Empire State Building - nuff said. One note, from the street, it looks like every other building. The first time I went there, I walked past it a bunch of times and never knew it. You have to know the address and look for signs.
Statue of Liberty - ALSO nuff said. You need to take a ferry though and the lines are HORRIBLE. Honestly, you can see it from Battery Park, so really....the trip over to the island isn't that great. You can also get to Ellis Island from Battery park, but same deal.
St. Patrick's cathedral - even if you're not religious.....its worth a quick stop.
Times Square - honestly, I hate it there. BUT, if you get one shot at NYC...you have to go through and walk down 34th st. BE CAREFUL THERE - it is PACKED with tourists basically 22 hours a day and that means it is also packed with people trying to get your money one way or another, through fliers or pickpockets. Now...it really isn't that bad, but it is bad enough that you need to be careful and watch yourself. If you LOOK like a tourist, you're a target. Targ...err...tourists do things like take cash out in public, stare at maps, stare UP, take lots of pictures......but then, these are things that travelers should just know anyway.
Penn Station - another one worth a quick stop, it is kind of out of the way, but its cool to see. There's also a cool mall in there and Macy's is real close.
In the summer....Ride the BEAST! It is a speed boat tour up and down the hudson, SO much fun! The guys that run it are are really funny and the trip is just all around cool.
Broadway show - seriously, if you're going there, you HAVE to see a show. It can be expensive, but there are ways around that. There are shows for everyone too. Avenue Q, Wicked, I love you you're perfect now change, Blue Man Group, STOMP, and on and on and on. For cheap tickets, TKTS is a MUST, they sell half priced and less tickets day of and day before. There are two booths in the city, one in Times Square where the lines are horrible and tickets are tough to come by. BUT, the little known secret, there's a booth at South Street Sea Port, and NO ONE IS EVER THERE. You can walk right up and get your cheap show tickets no problem. Plus, going on a weekday will save you money.
I could honestly go on forever, I love the city and spent as much time as I could there. Please let me know any other questions you may have - I also have LOTS more suggestions and my own little things that I loved to do. Including restaurants, little known sites, bars, etc. One of my favorite things was the Beatles tour....being that you're British, that one might be of interest.
