An extended period of recreation and or tourism spent away from home meets the definition of a vacation.
The Nixon administration during the summer months would move the Presidential operations to San Clemente, California to the "Summer White House." Nixon's Secret Service detail lived on the Summer White House estate. It wasn't a vacation.
LBJ would at times would micromanage the Vietnam War and drink a lot of beer from his ranch in Texas. It was not a vacation.
Reagan ran the country from his ranch above Santa Barbra. No tourism involved and the only recreation was chopping wood. It was not a vacation.
G.W. Bush ran the government and met heads of states at his ranch in Crawford Texas. No tourism and splitting logs and clearing brush isn't really fun as a recreational activity. The Secret Service had it's own bunk house. It was not a vacation.
If Obama's Secret Service detail has to be put up in hotel suits, it's probably a vacation.