Sadly hotels in New York are ridiculously expensive - you might catch a last minute deal somewhere, but you'll be looking at 100+ per night easily. I just did a quick check on a popular hotels website and 4 nights at a decent place is going to be just under the £800. Check across a few of the hotel sites for best rates (and check the hotel's site itself, sometimes they're cheaper).
Try and get a hotel near a subway station - you'll be doing a load of walking anyway, the last thing you'll want to be doing at the end of the day is another 20 minute hike to your hotel.
I'd advise against staying outside of Manhattan - it's not that much cheaper and you'll be stuck with all the other commuters in the morning/evening. You want to be straight up and into Manhattan in the morning!
Take the reviews on Tripadvisor/Yelp with a pinch of salt. There seems to be loads that get bad reviews simply because the furniture wasn't to their liking or there wasn't ice available one evening...
Few hotels that I've been to that I can recommend: the Pod hotels (small rooms but you don't need anything massive, you won't be staying in your room!), Hotel 31, The New Yorker, The Pennsylvania, Herald Square Hotel, Sheraton Tribeca and 4 Points.