Often implies actually moving or looking in different places, not just thinking or planning. She looked around for a place to sit in the crowded cafeteria.
Pro Tip 2/3
Urgency Implied
Suggests a need or urgency when searching for something missing or required soon. He was looking around for his passport frantically before the flight.
Pro Tip 3/3
Casual Contexts
Commonly used in casual or informal situations, rather than formal or official ones. After the game, we looked around for a place to grab a bite.