I would like to create a (preferably conformal, but not necessary) curved grid like this:
trying to match the outline of a curve I have:
Kind of like the lines on an athletics track, but a grid. How can I do this? Any program is fine.
Looks like a candidate for Illustrator's Blend Tool:
Here's what I made with the Blend Tool based off your image:
This will easily create the concentric dividers. You can then manually add in the radial dividers by hand if you require them.
You can also try Photoshop's warp tool to manipulate on what you're trying to achieve: