I have brought my bike inside and I have seen it done many times by others.
At the grocery store, I lock up outside as there is a bike rack near the cart pen.
At Cafes, convenience stores, and restaurants is where I will consider bringing my bike inside. In those cases I prefer to have eyes on my bike. It is generally not an issue.
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My stable:
2013 Redline Conquest CX
2010 EasyRacer GRR
2015 Cruzbike Vendetta
2009 Raptobike Lowracer #0067
My blog
My bike pictures