Hello Amit,
February/March is still the winter time in the U.S. In some of the cities you want to visit you can expect to encounter cold weather and possibly snow. Here is the monthly average temperatures for New York City. http://weather.msn.com/monthly_averages.aspx?wealocations=wc:USNY0996 You can expect to find similar conditions in Washington DC.
Averages for San Francisco http://weather.msn.com/monthly_averages.aspx?wealocations=wc:USCA0987&q=San+Francisco%2c+CA+forecast:averagesm It will be about 10 degrees fahrenheit warmer than in the Northeast. But you can still expect some chilly days.
It is possible to encounter some temperate weather in LA during those months. http://weather.msn.com/monthly_averages.aspx?wealocations=wc:USCA0638&q=Los+Angeles%2c+CA+forecast:averagesm The weather in Vegas will be within a similar temperature range.
A temperature conversion tool can be found here. http://www.onlineconversion.com/temperature.htm
With a 14 day visit, you will need to fly from coast to coast to see all of those cities. It is over 2,900 miles (4660 kilometers) between New York and San Francisco. You can take the train between NY and DC. Both are cities that are best visited without a rental car. On the west coast you can either drive between, San Francisco, LA and Vegas or take the bus or train.
$100 per night for a hotel in any U.S. city is not reasonable...especially if you want to be in a comfortable, safe, centrally located hotel. In NY you should expect to pay over $300 a night. Hotels in the other cities may be a bit cheaper, but still well over $100. I recommend that you search for hotels using our Hotel Booking Engine. This will give you an idea of what you can expect to spend. www.usatourist.com/english/reservations/reservations-hotels.html
From the questions you ask, I am thinking that it may be better for you if you keep your visit to one region of the United States. By wanting to visit cities on both ends of the country, you can expect to spend about $1000-500 more on airfare for you and your wife, depending upon whether you will travel round trip. It may be better if you used that money towards your lodging. Also, if February/March is the only time of the year that you are able to visit, you would probably be better visiting the southwest, where it will be warmer. NY and DC in winter can certainly be nice. But if you are not used to those conditions, you may want to keep those cities for another visit during the summer months.
I hope that this helped you. No matter what you decide, I am sure that you will have a wonderful trip. Hopefully it will be the first of many visits for you!
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