<blockquote>Quote<br><hr>the only bad part of town is Times Square... but if you're set on staying there go for it<hr></blockquote>I think it is reasonable to advise first-time travellers that there is no need to stay around Times Square just because so many tourists do, and so many hotels are in the region. There are plenty of good hotels and hostels in other, more interesting parts of Manhattan (however the differences between neighbourhoods are sometimes rather exaggerated, it has to be said). Lots of second-time travellers do realise other areas are preferable. But your comment is not very helpful for the tourist who can't be expected to interpret your comment as a personal opinion or dislike, rather than as a more objective bit of information on relative badness (and erroneous at that).
A quick look indicates you might think about $250/night before taxes. The rather nice Fitzpatrick Grand Central starts about $260. The cheap Pennsylvania hotel at the railroad station/Madison Square Garden apparently caters largely to tour groups and foreign tourists. I've managed to find better options in the past, but I'm amazed that it seems to be asking $200. It's worth about $100.
I guess the lesson is that New York's price inflation makes Chicago an attractive destination. Even Tokyo!
The Portland Square Hotel has availability on your dates for slightly less than $200 a night and it's in the area you want - on47th Street, between Broadway and 6th Avenue.
Further towards downtown but still within your budget (and with availability on the dates you mention) are the Herald Square hotel and the Hotel Pensylvannia. I've heard a lot of good things about the former in particular.

Thanks for your help. I am a repeat viisitor and didn't think Times square was a bad area at all - you should see some parts of Glasgow! I just think it's a really handy location for shops, restaurants etc. I've made the mistake of checking out the hotels I've been looking at on Trip Advisor and as soon as I've found one I think looks good then I read terrible reviews. I would consider other locations as long as they were close to a subway stop and handy for everything with restaurants close by.

you can get a nice room at the Sohotel on Broome Street (Lower East Side) for about $160. It's not very close to the typical "sights" but it's near subways (a 7-day metro card is only $24) and lots of good eating/small concert venues/bars/nightlife/shopping, Chinatown, the Village, Soho, and Little Italy. Non of these are "bad parts," however, the streets are not numbered. Sohotel
You can also stay 2 blocks off in Times Square at the Paramount, a very cramped boutique hotel, for around $270, although it's TIGHT and dark and, I think, not worth it.

#13 - If you wanted to go see a play on Broadway every night maybe staying in Times Square again would be a good idea, but since your main concerns are shops and restaurants maybe you ought to check out a different part of town this time around. As long as you're not staying towards the extreme East or West Side, where there probably aren't any hotels anyway, you ought to be within about 5 min of a subway. Though no other place will be close to the number of lines that stop at Times Square.
The Sohotel mentioned above would be a good area to stay, the Hotel 17 would be too.
The Hotel Pennsylvania has received its share of criticism here in the past...

Unfortunately it seems some people are coming off with a bit of attitude. To clarify the point I think many are making here (which, to be honest I wholeheartedly agree with) is that Times Square is a "bad area" in the sense it's the most boring, sterile and uninteresting part of the city, with a side of sleaze around Port Authority station. When I lived in NYC I avoided Times Sq like like the plague. However to each their own, if you enjoy Times Sq, go for it, but the area is very overpriced.
NYC's subways are very extensive and easy to use, so I'd reccomend staying below 23rd St. Besides, if you're looking for interesting shops and restaurants you're better off somwhere between 23rd St & Houston. Times Square is mostly just corporate chains. Personally I'd say see more than Manhattan and get a place in the Brooklyn Heights area for less money, there are half a dozen train lines leading to mid town from there.

Brooklyn Heights has cheap hotels? That's the most expensive area of Brooklyn, if there are any hotels there I can't imagine they would cost any less than a number of hotels in Manhattan.
I'd agree that if the OP hasn't seen been to the Brooklyn Heights Promenade and walked over the Brooklyn Bridge, that would be a great thing to do this trip...