There is no one "best" location. It depends upon your likes/dislikes really. If you tell us more about yourselves (what you like to do, whether you want a more casual trip or are intending on doing a lot of fine dining, theater etc.)
There are a few kinds of apartment hotels:
>a traditional hotel that has some suites--this would require your phoning or emailing for details and prices from larger hotels like the Hiltons (or any hotel you like)
>an all suite hotel
The http://www.affinia.com chain has 7 hotels, all with rooms that will have kitchenette. The most upscale is the Benjamin in midtown east (not far from Rockefeller Center) but the Affinia Gardens is also very nice and somewhat newly renovated. It's on the edge of midtown and the upper east side, a bit more residential area but also near more "local" shops and restaurants.
Other all suite hotels that are nice include:
the San Carlos
the Blakely (not all suites but some)
the Kimberly
>then there are townhouses (smaller buildings that were once single family homes) that function as inns.
1871house.com mentioned above is one of those and is on the upper east side nearish the Affinia Gardens. These inns have more charm and sometimes extra features like outdoor space, but the downside is they don't usually offer daily maid service (maybe once a week since you're staying for 2 weeks) and there's no "front desk" or concierge for making reservations etc. Some other very nice smaller "inns" with apt like suites are:
on the upper west side, another nice residential area
http://innnewyorkcity.com
http://countryinnthecity.com
http://wymanhouse.com
in Greenwich Village
http://west-eleventh.com
http://abingdonguesthouse.com
http://www.gvhabitue.com/
>last, there are some regular apartments. One that I know others have enjoyed which has a great view is
http://bigapplegetaway.com
but it doesn't seem to be available for 2 weeks in May.
This co.
http://www.hotelaka.com/
has some gorgeous looking apartments in very nice locations (I especially like the Central Park location) but I don't know anyone who's stayed there so can't vouch for whether they're as good as they look. They are quite expensive vs. other options but probably would fit your budget.