I have seen a lot of ladies adjust theri rates when they travel but not all do. You need to cover your travel expenses but also price yourself within the market that customers will pay. EC made some good comments of how it can work both ways.
I have seen some ladies hold their rates no matter where they were, and others that adjusted for the market. For example, I knew a las Vegas provider who was 300/hr at home, but when she came to Hawaii she charged 350. I think she charged 400 in another market, then she was 200 in Kansas, and 250 in Oklahoma City. On the other hand I have seen some 600 Los Angeles ladies maintain the rate in other cities.
I think what doesnt work is raising your rate above your normal rate and above the area average when you tour. As an example of that, there was a popular Chicago lady who charged 300/hr in Chicago. She announced a tour to Hawaii but put her tour rate at 500/hr. The average in Hawaii is probably 350. Guess what? She got no interest and cancelled the trip. Now I think if she kept her home rate of 300 for her tour or bumped it slightly to 350, she would have done very well on a Hawaii tour. On the other hand, if her Chicago rate was already 500, and she was well regarded and well reviewed there, she probably could have come to Hawaii at 500 and still do okay. The problem was trying to jack up the rate above her home rate and above the local rate just for the tour.
In your case I think you could definitely up your rates in NY or LA or Vegas, and either maintain or lower slightly for Atlanta, Carolinas, Florida, etc.