Anything not kept in cabinets is going to require washing before use to be hygienic, and near a cooktop, this is especially true. Dust mixed with grease is rather unappetizing, too, so even if you use the open shelving for decorative items rather than practical ones, you will still be washing them frequently. One way around this might be to consider lighted, full glass front cabinets with glass shelving, so all you would have to keep clean would be the doors, not the contents, while still having the more open look. See Houzz Photos under "lighted glass cabinet" for examples.

That was my concern. I don't think I will be having the open shelves near the stove.

i dont have open shelves near the cooktop as it *seems* to me that they would get dirty. my open shelves that are 5' away are fine tho.

I have open shelves on either side of my kitchen sink. There is an island in the middle , and my stove on the other side of the kitchen. I do not have an problems with grease, because the shelves are on the opposite side of the kitchen. I have small open shelves and hooks for coffee cups on the bottom of the cabinets that are to the side of my range. Because we use the cups everyday, they are constantly used and washed, grease isn't a problem. This is our beach house, and our guests never have to ask us where glasses or plates or anything is, because they can see it on the open shelves!