Sounds like an ambitious awesome trip Yab Yab. I have a few ideas for you.
21st Jan to 27th Jan - San Francisco-I see you are interested in Yosemite. I hate to tell you, but before you leave San Fran you may want to see if the park is open. A majority of the park is shut down due to snow. Yosemite Village is probably going to be awesome, but it does not shine to the whole park itself. Still worth the 6 hour drive. I highly recommend renting a car and driving down Hwy 1 toward Santa Barbara. Even in the rain and drizzle of the winter this coastline is some of the best in the world. Have you thought about maybe taking Amtrak up to Seattle, Wa? My son and I recently did this. It was only 75.00 apiece, but did take 24 hours to get there...and 24 hours to get back. Well worth the trip. You were able to sit back and relax while someone else did the driving. That is just a thought. 6 days is a lot of time in San Fran alone.
28th Jan to 31st Jan - Las Vegas- Vegas is a site to see in itself. I do recommend Grand Canyon, but again the snow may close down part of the Canyon. It is an awesome site to see. It will take you at least 4-5 hours to get to the Canyon from Vegas. I did a search and you have several choices for Las Vegas shows. The average prices are $66-160. I highly recommend a Cirque themed show...you have three choices. KA' by Cirque Du Soleil, ZUMANITY by Cirque du Soleil, Le Reve - Aquatic Spectacular, Disney's the Lion King, Blue Man Group, and Carrot Top (Comedian).
I do not think you can go wrong with any of the shows. I hope you got a good price for your hotel room in Vegas. This is the only place that it is cheaper to stay in a Casino than staying in a hostel. You can sometimes find a room for $12.00 a night. I could not find a hostel cheaper than that. At least not at the per person price. It is definately worth staying on "The Strip". The walking that you will be doing up and down the strip is tiring.
1st Feb to 9th Feb - New York New York is one of my favorite cities! I highly recommend the 48 hr hop on hop off double decker Sightseeing bus that includes Empire State Building and Statue of Liberty/Ellis Island Tickets for $83.00. I provided the link- http://www.newyorksightseeing.com/tourpage.php?item=ENS . NYC will be freezing by that time so definately dress in layers and appropriately. I would recommend a Broadway show while you are there. You can go to the Tickets box office in Times Square and get awesome same day sometimes half price tickets.
Washington DC is a place I have not spent much time besides the basics. There are numerous free museums there that you can get lost in. Maybe take in an IMAX movie? How are you getting from Washington, DC to New Orleans? Renting a car or driving? Considering I am a true Southerner I would be disappointed if you missed our great Smokey Mountains which are located in Tn, NC, SC, and Eastern Ga. If you are flying I guess you can't help it. Just promise to some day come see us
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New Orleans is a nice enough place. I wish you could of seen it before its Hurricane Katrina days. It is working very hard to restore itself. You will definately have to try a Shrimp PoBoy or some grits while you are there. Not to mention Benets (I know I didn't spell it right) and some Chikory coffee.
San Diego I called home for ten years. It was and still is my favorite city in the World. Please do bypass Tijuana, Mexico and go to Rosarita or Ensenada, Mx. Tijuana is full of crime. You will enjoy the other two cities just 30 minutes south of TJ.
I do wish you a lot of fun and nicer than normal weather. Any questions feel free to ask.
Kim