One month should be enough for a nice trip. I would spend about a week in New York City then fly to California for nearly three weeks of travel in the Southwest.
February will be in the dead of Winter.
New York City is likely to be bitter cold with a possibility of snow. If you are lucky, the weather will be mild (above freezing) with daily sunshine and cold nights. If you are unlucky, the temperatures can be extremely cold with bitter winds that chill you to the bone even through heavy clothing, and severe snowstorms can cripple the city with a foot of snow.
In California, you will find much more hospitable weather conditions. San Francisco can be chilly in the daytime, with either sunshine, fog or rain, and cold at night, but above freezing. Los Angeles will be a bit warmer, with daytime termperatures that can vary from pleasant to chilly, and nightime temperatures that will vary from chilly to cold. It will not fall below freezing.
Las Vegas is likely to be fairly pleasant. The daytime can be warm enough to venture out in light clothing, but the nights will likely require a jacket or pullover. (Last winter, Las Vegas was hit with a freak winter storm that dumped 3 or 4 inches of snow on it and crippled the traffic for several days. That was, however, extremely unusual, and happens only once every five years or so.)
I suggest you explore the coastal highway in California between San Francisco and Los Angeles. Monterrey, Big Sur and Santa Barbara are all beautiful locations along the coastline. Yosemite offers exquisite mountain vistas, but will requre you to venture into the mountains and brave the hazards of winter driving through snow country.
Las Vegas is a wonderful adult playground with over-the-top architecture and entertainment on an extravagant scale. It is also near some great scenic attractions. The Grand Canyon, Zion National Park and Bryce Canyon NP are not far, but they would also require some driving through mountainous snow country. Death Valley is only two hours from Las Vegas and would not require any snow-country driving. The climate of Death Valley is most pleasant in the winter when the intense heat abates for a few months.