Let me be the first to tell you....short term rentals (under 30 days) are generally illegal in NY. Others often recommend apartment-like hotels, such as the Affinia line to people who want a "suite" with a kitchen.

Rentals less than 30 days are almost all illegal. (They can be legal only as part of single family houses - which are extremely rare in Manhattan - and the ones that exist are worth from $4 million up - way up). Many are advertised on Craig;s list - and many are scams. Check out the Affinia group of all suite hotels.

Also be aware that your visit will be at the busiest and most expensive time of year - so don't expect any bargains. And do try to reserve something now - since prices will generally only go up over time.

Check RCA apart-hotel too.

Not in mid-town, and probably not a budget choice but perfectly situated is the Beacon Hotel on the UWS.

Book something cancellable asap, you can continue to look for bargains between now and then but that's a busy time in the city.

Should have added the Milburn Hotel and the Salibury Hotel.

The Affinia group of hotels has several suite hotels with apartment-style units (with kitchens). The cheapest tends to be Eastgate Tower, which has, I believe, some larger units with 2 baths, something almost unheard of in NYC.

"RCA" apartments is Radio City Apartments. Good location, but you'd need to book asap.

Realize that rates are at their highest of the entire year the week before Thanksgiving.

How many days is the rental? Yes, it is illegal, but you might be able to do it in Queens, Staten Island, Brooklyn. Some private home owners could agree to it.

Or look for apt exchange. You give them your place in London, they give you theirs in NYC. My bro has been trading homes for 2 years now. Ifcourse, watch out for theft and damages, etc.
Overall, it might be cheaper and safer just to stay in a hotel rather than risk eviction or arrest at a temp rental, or letting strangers stay in your home.

The only place a rental would be viable would be in New Jersey! You could try there....but that would be quite a hike, no?

This whole discussion about the ins and outs of vacation rentals in NYC seems fruitless to me. They are illegal. Period.

Look for a suite hotel and save yourself the hassle. If you end up booking some scam on Craigslist, you have only yourself to blame. I have only come to realize fairly recently how big the idea of vacation rentals has become; so many people only do those for their vacations. Unfortunately, that's just not possible in NYC. Since 2-bedroom units are rare in NYC suite hotels, booking soon is your best avenue. And then you can keep looking for cheaper alternatives if you book something that can be cancelled without penalty.