You probably want to remove the granite backsplash if you are going to tile it, otherwise it looks like an afterthought, it is normally one or the other. As far as the vent, you need at least an 1/8" clearance to get it in.

Thank you, from the picture it is hard to see, but what looks like a granite back splash is the glue from the old back splash that we removed.

When a kitchen has a granite countertop with movement or pattern to it, as yours does, I recommend a solid colored backsplash. Your kitchen looks very classic and beautiful with thew new countertops and white cabinets, and you don't want the backsplash to compete with the granite. I would use a subway tile in a pretty pale gold or ivory to tie in with the counter. You could use a ceramic with a bit of texture to it, like the crackle glaze finish offered by Sonoma Tile Makers in their Stellar line (one of my favorites). You could also use an ivory travertine as long as it didn't have a ton of veining in it. I can't tell if you've picked a wall color yet, but you could paint the walls one shade deeper than the backsplash.

As for the hood, you will probably need to use the smaller one as Norm mentioned above. I would take the backsplash tile up to the ceiling behind the hood...same for the window. It's a small space, so it won't add a ton of cost, and it will look much more custom and elegant than stopping at the bottom of the cabinets.

Your cabinets and granite are light, so maybe some interest in the back splash, and a little contrast in color and texture would be nice. It's hard to tell in the picture, but it doesn't look like you get a lot of natural light, so I don't think you want to go too dark though. Definitely add in some stainless colored accents with whatever you do to bring in your appliances and hood, and also some warmth to contrast the cool tones and bring out the warmth in your stone.

Here's just a few different examples depending on what look you are after.

Thank you, I do like the look of a subway tile, and will visit the Sonoma website. I was considering using a different tile behind the range, and do plan on bringing it up to the ceiling.

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Here are a couple of white kitchens with gold-toned granite that have back splashes I think look nice. I also love subway tiles and simple glass tiles (but not busy multi-color mosaics):

I agree...I would stick with a single material mosaic for the backsplash. I love the last photo that feeny posted.

Don't use an undersized hood as it will not do the job for you. BTW, a 30" cooktop is supposed to have a 36" hood. You can get away with 30" if you have to, but never 24".

Instead, have that small cabinet either reinstalled 1/2" over or even totally removed so you can fit in a 30" hood. Or get a stainless steel fabricator to somehow modify a 30" hood to fit. Seems like a pain but better just to suffer once today rather than every time you use the cooktop for the next 20 years.