The best advice is to bring as little "stuff" as possible. If you think about all the stuff you're bringing, you could categorize it like this:
- I will definitely need it in the airport or on the plane (Eg passport, money)
- It will make me more comfortable in the airport or on the plane (eg pillow, book)
If it were lost, stolen, delayed or damaged my trip would be pointless or ruined (eg laptop)
If I check it I will have to pay a baggage fee or wait for it to come out on the belt
Try to restrict yourself to items "above the line". Now what you're dealing with in the stores, the bathroom, at security and so on is a large purse or a small backpack and not something on wheels that a store might be likely to ban.
Of course if you're travelling with another person, it's such a luxury to leave your stuff with them while you pop off to do something.
Many business lounges have small lockers - you can't get a rollaboard in them, but you can get a backpack in, and I have used that to stash my carryon while I spent a layover exploring a city. It's overkill for wanting to go shopping, but something to keep in mind if you have a long time to spend in an airport. (I believe they're designed for you to put your stuff in while you shower, or to simplify wandering around the lounge getting food, drink, and reading material without wanting to drag all your stuff around.)