I am not sure how that will look...There really needs to be space between the hood and the cabinets next to it. It also depends on the size of the doors on the right of the hood... a floor plan would be nice ... it will be easier for folks to help!

Open shelving is popular in that situation.

Definitely put a 12" on the left with 3" clearance to the hood. The left side of that cabinet should line up with the left of the lower if that is the end of the cabinets on the wall.

Sorry yes, the 12” leaves at least 3” clearance to the hood. I can post the whole plan-was just hesitant as you know how it goes here. Folks start answering questions you haven’t even asked and the original issue gets lost in the abyss :).

I like uppers on both sides, particularly if the doors are the same size

I would choose a voided door cabinet with finished interior. Better than floating shelves. Better usage with NO door for a shelf of cookbooks/a shelf for mugs or bowls or small plates///napkins//stuff you grab frequently or just would like in the open type of cabinet. this will be a 15 in wide cabinet it appears......it could also be a frosted or seeded glassdoor. This is a nice cabinet in a good spot.....go ahead with the idea.

I have a 12" upper next to my vent hood. We used it for oils and vinegars, it was a perfect size and placement for that. New kitchen has a pullout for those things, though.

When we move back into our kitchen I think we will use it for bowls (pasta plates) on the lowest shelf because that will be easy to grab from and plate up dinner. At the top will likely be the odd stove accesories we don't use that often (wok ring, simmer plate) and in between is probably travel mugs because its the right size and I don't have a great solution for those.

My point is ... a small cabinet often fits those small collections of frequently used things that don't fit well in other places. I vote for a cabinet, even if it is only 12" wide.

I would eliminate the uppers by the range hood completely and tell hubby he needs to learn a little about balance there is none there with or without the skinny cabinet. BTW storing oils beside the stove is the worst place possible.

@Patricia ... I agree that storing oils near a stove can subject them to additional heat, BUT not the case in a closed cabinet to the side of an exhaust vent. I was concerned about that as well, but I used a temperature sensor with logging capabilities to track the temp in that cabinet over a week compared to the rest of the house. Even when baking, the temp in the cabinet was no worse than 4 degrees F warmer than the rest of the kitchen.

I can see the concern, but just FYI the data doesn't prove it out. Wood is a decent insulator.

If possible, try to get more landing space on both sides of stove. Ideally 15" minimum.

But if it must stay then...

Before making any decisions, check the stove and hood installation instructions to determine height and Spacing for combustibles (cabinets above)

Then

Try to keep some type of symmetry around the hood.

Same spacing on both sides of hood.

I prefer 3" of Spacing around hood.

Then same width cabinets on both sides if possible. A 1 door wall cabinet opening away from hood is nice, to avoid reaching around door, if using while cooking.

If the sketch you posted is the only option, then I would do 3" of Spacing then a 1 door cabinet then the 2 door cabinet to right make the door same size. Example if 12" x 2 doors = 24" wide cabinet with 2(12" doors)

Also, if cabinets against an adjacent wall, don't forget the functional filler, so the door will open and the hardware won't hit wall.

I agree that some adjustments need to be made. Here are some examples of kitchens with offset hoods etc.

How about this adjustment? You haven't shown us the rest of the kitchen so it's hard to be more helpful than this.