We are spending 4 days in New York & 4 days in Washington after a cruise. As we want to see as much as possible in that time we want to try and get a self contained apartment close to metro lines. Which areas would be best ? Also can anyone advise if it is best to buy the train ticket from NY to W and then Washington to Chicago on line before we go or direct from the train stations when we arrive.
Any advice would be appreciated.

Short term apartment rentals are illegal in NYC (I don;t know the rules in DC). If you want more room than a basic hotel room you should look at one of the hotels with suites.

Check out:

Radio City Apartment - a hotel in a great central location but basic - and often sells out months in advance
Beacon Hotel on the upper west side
Affinia group of all suite hotels - moderate prices and a host of different suite configurations

If you tell us when you will be here and what your budget is people can make specific recos.
And most hotels in NYC are near a subway (we do NOT have a Metro).

Amtrak has regular service and the Acela from NYC to DC. It is matter of time and money.

Which areas would be best?

In DC - Dupont Circle, Penn Quarter, Downtown
Possibly less expensive (if this is a concern) In VA - Rosslyn, Crystal City right across the river.

Amtrak's abbreviation for Washington Union Station is WAS

Amtrak tickets get more expensive closer to the date of departure

If you buy your Amtrak ticket for NYC to DC more than 14 days before your date of travel, you will receive a 25% discount.

If you know your dates of travel, it's definitely better to buy your train tickets as far in advance as possible. The question is whether you want an assigned seat in a more comfortable and faster train between NYC and DC (Acela Express) or a regular "reserved"---though unassigned---seat on a regular train.

Get your train tickets (NY to DC) ASAP.

I would fly the DC to Chicago leg. It's cheaper and much, MUCH quicker.

For DC apts:

http://www.homeaway.com/vacation-ren...ngton-dc/r5000

Look at "Capitol Hill rentals", "Downtown Washington DC rentals", and "Dupont rentals". Come back with specific apartment links and we can tell you if the location is good (not all are).

Yes ... I would like to echo Bardo1's point about flying from DC to Chicago. And you should price tickets on Southwest from Baltimore to Chicago-Midway as well. You can easily get to Baltimore on Amtrak.

In the DC area many self catering places don't rent for short weeks, or if they do, the nightly rates will exceed those of suite hotels which include kitchens.

In DC, this B&B has a self-contained apartment with a kitchenette and private entrance for just $295 per night:
http://www.dupontatthecircle.com/rooms.html
It's ideally located, very near the Dupont Circle Metro stop.

Thanks to everyone for the valuable info. We have found some good accomodation in both NY and Washington.