As you have asked about the top universities for design in the world, I am mentioning some of them, check below for the details

Pratt Institute | Brooklyn, New York
Location : 200 Willoughby Ave, Brooklyn, NY 11205, United States

New York School of Interior Design | New York
School Location : 170 E 70th St, New York, NY 10021, United States

Florence Design Academy | Italy
School Location : Via dei Martelli, 4, Firenze, Italy

The Interior Design School | London
School Location : 22 Lonsdale Rd, London NW6 6RD, United Kingdom

University of California (UCLA) | Los Angeles
School Location : Los Angeles, CA 90095, United States

Harrington College of Design | Chicago
School Location : Madison Plaza, 200 W Madison St, Chicago, IL 60606, United States

Vancouver College of Art & Design | Canada
School Location : 626 Pender St W #500, Vancouver, BC V6B 1V9, Canada

Interior Designers Institute | California
School Location : 1061 Camelback St, Newport Beach, CA 92660, United States

Dublin Institute of Design | Dublin
School Location : 45 Kildare St, Dublin 2, Co. Dublin

Hong Kong Polytechnic University | Hong Kong
School Location : 11 Yuk Choi Rd, Hung Hom, Hong Kong

The Art Institutes | Canada
School Location : Canada

Edinburgh College of Art | UK
School Location : ECA Main Building, 74 Lauriston Place, Edinburgh, Midlothian EH3 9DF, United Kingdom

Bellevue College | Bellevue
School Location : 3000 Landerholm Cir SE, Bellevue, WA 98007, United States

California State University | Sacramento
School Location : 6000 J Street, Sacramento, CA 95819, United States

College of Southern Nevada | Las Vegas
School Location : 700 College Dr, Henderson, NV 89002, United States

Lorenzo de' Medici School | Italy
School Location : Via Faenza, 43, Firenze, Italy

Istituto d'Arte Applicata e Design| Italy
School Location : Italy

Academie Grandes Terres | Paris
School Location : 5 Rue de Charonne, 75011 Paris, France

Creapole Ecole de Creation Management | France
School Location : 128 Rue de Rivoli, 75001 Paris, France

Whitehouse institute of design | Australia
School Location : Level 4, 672 Bourke Street,Melbourne, Victoria,Australia, 3000

The Art Institute of Fort Lauderdale | Florida
School Location : 1799 SE 17th St, Fort Lauderdale, FL