You have a good RV for visiting cities however if you want to spend six months in each city you'll probably want to do as Parrothead Mike suggests - stay in a RV park outside the city, then use your car (rent one if you don't tow)or take public transportation to get into the city.
We've visit a lot of cities including all the ones on your list except San Francisco. We don't stay for a long time, maybe a week. We usually stay at Walmart or a casino because they're close to the cities and then we drive our RV into the city for the day. We're interested in history, parks and other attractions but not nightlife.
You'll find information about Las Vegas, New Orleans and a little about Austin on my blog however we visited the other cities before I started blogging so all I can tell you is that finding a place to park can be a challenge but Google maps and street view are a big help. Las Vegas and New Orleans are both super easy. The best way to see New York is to stay at the Liberty Harbor Marina in New Jersey and take the ferry across. The RV park is expensive but worth it if you want to see the city.