show (someone or something) around
1. To introduce and guide someone through some place. This is where you'll be working, but let me show you around the rest of the building. My sister's coming to visit from America so I'm going to show her around.
2. To display something to a variety of different people. He never thought someone would steal his idea when he started showing it around. I'll be showing my paintings around to various art galleries over the weekend.
show someone around (some place)
to give someone a tour of a place. I'm very glad you've come to work here. Let me show you around so you'll know where things are. Welcome to our town. As soon as you unpack, I'll get someone to show you around.
show around
v. To introduce someone to some place by visiting various locations: The real estate agent showed us around the house. The guide showed us around the old part of the city.