You can travel full time and remain a NY resident until you get rid of your stuff. Once you no longer have a connection to NY you will want to look at becoming residents of FL, TX or SD (in that order). SD does require you to spend 1 night at a campground in SD to qualify. There can also be health care issue in SD so be sure you make a good choice. FL is the best domicile (IMHO) based on cost. All 3 States have no State income taxes.
You don't need to setup and kind of relationships at any of these States, just go there, get DL and vehicles registered and then hit the road!