I'm putting your overhead layout drawing here for convenience:

I went through the same thing that you're talking about. I was pretty much my own lighting designer, so I depended tremendously on what I could find online. I found this advice helpful:

experts123.com says, "For general lighting applications a good rule of thumb is to space recessed fixtures a distance that is equal to about half the ceiling height. For example, if a room has an 8ft ceiling, you should probably space the recessed fixtures about 4ft apart. This rule of thumb should be used only as a base line."

I see you will not have wall cabinets around the sink area. With no opportunity to install undercabinet task lighting here, I would want cans positioned over the countertops for task lighting. I am *not* an expert, but I would be tempted to center a can over the sink, and then, using the aforementioned rule-of-thumb as a guide, space the rest of the cans appropriately.

I would include undercabinet lighting on either side of the cooktop. I imagine that UCL coupled with your hood lights would be very dramatic.

Of course, you need to also adjust that plan for any decorative lighting that you plan to include. Here's a pic of my finished kitchen as an example:
{{!gwi}}
I have 9-ft ceilings, so I figured about 4-4 1/2 ft spacing for the cans. Then I adjusted their placements according to where we wanted the ceiling fan (roughly in the middle of the kitchen) and the pendants over the bar.

I hope this helps.

Start in the middle -- decide if you are you doing a decorative fixture(s) there, and pick one, and figure out how much light it/they will put out. Then fill in the cans around it accordingly.

I didn't have the budget to tear out my entire ceiling, so all my can lights are in their places from the old kitchen layout. I have two cans about 4 inches from the wall, and two about 3 feet from the wall, and one in a very odd spot about three feet from one edge of the corner and two from the other. It's not too bad looking, because they are spread out nicely and not crowding my center fixtures. (Also, the two "too close" to the wall are hidden by a beam I couldn't move.)

It's not ideal, (I'd love to move one of the side cans centered on my pantry), but there is a lot of room for "good enough" on the scale from "perfect" to "swiss cheese," and my kitchen has plenty of light.

Here is a link that might be useful: {{!gwi}}

UPDATE - We wound up putting four cans above the cooktop wall countertop and four cans above the sink wall countertop. Placed at countertop edge (as distance out from the wall). We also placed two cans along the fridge/oven wall and two down the center. We used 6" LED EcoSmart bulbs and they are amazing!!!

We also have two 48" LED UCL bars running under the two sets of uppers...one on each side.

All of these are on dimmers so adjustable per time of day and per person's preference.