And yes, a white sneaker that is flat has a more street vibe than the ones a little bit higher made for running or other exercises. They look more polished and put together.
Having said that, here are 6 ways to wear your white sneakers

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With that perfect summer dress. Printed or in a solid color. Short, midi or maxi. Flowing or more body conscious. The same can be said to skirts. They all could make a great duo with a white sneaker.
And yes, the look here is pretty casual but you can give a little upgrade on it. Just have a look at the looks below:

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Those looks are a little bit dressier than the ones before but still pretty much casual. The skinny jeans, the tapered cuffed/cropped pants, the leggings… all great options to rock the white sneakers. Other pants like tailored ones, bootcuts and straight pants are also a possibility.
On the top, tunics, flowing tops, sweaters, t-shirts, blouses, camis and shirts are good options. Cardigans, blazers, coats and jackets are all welcome.
One good idea is to pair your white sneaker with an all black look. It gives a chic, dramatic vibe. Or a look with all light shades that makes a much more smooth look, but quite elegant.
Take your pick.