His destination? Art Basel in Switzerland, considered the premiere international art show for modern and contemporary works.
"Yes, Brad Pitt visited and had lunch here," communications manager Peter Vetsch told PEOPLE.
Although the show was not yet open to the public, Pitt (a notorious art buff) enjoyed a special showing of stylish furniture from the '40s, '50s and '60s at the Design Miami gallery.
"Brad asked questions that only an art expert would ask," Wendelin Lang, who organized the exhibit, told Blick, a daily Swiss newspaper. "You can feel that he is an absolute maniac."
After the furniture shopping, Pitt reportedly enjoyed lunch – a tuna burger and two Coke Zeros – in the Art Collectors Lounge. "He looked deep into the eyes of the staff," his server, Erna Zürcher Lüscher, told the paper. "His charisma is just super."
The actor and Jolie – who are expecting twins this summer – recently signed a long-term lease for a chateau on the French Riviera.
After the visit, Vetsch said, Pitt hopped an evening flight back home – just in time for Jolie's 33rd birthday on Wednesday.