A few hotels have purpose built two bedrooms suite with more than one living area and other fun things like media rooms, kitchens, office etc..... Waldorf Towers, The Lowell, Trump, Plaza Athenee, Ritz Central Park, Chatwall and Mandarin come to mind right away, but afraid that some of those suites I have booked in at for way over 2k.
Yes, in my searches I came across more than a couple of fabulous suites that were PERFECT for us, but sadly exceeded my budget by a factor of 10. Oh well, perhaps one of us will win the Euromillions this weekend.
Good point about the hotel style. When I wasn't finding too many possibilities it seemed less important, but given the wealth of options that have been suggested here I'll obviously need to do a bit more research.