So I recently put down 4" of double cut down around my yard. I moved the mulch back away from the tree trunks by a few inches because I know that's bad for them. Should I put anything in that gap so the mulch doesn't fall back in? Basically it looks like a 4" doughnut where the trunks are. I'm okay with it but wasn't sure if putting a nominal amount of gravel would be a good idea.
No, don't put anything in the gap, the point of not having the mulch or anything else piled against the trunk is to prevent rot problems; the way you describe it though, it probably looks very odd. Its usual to gradually thin the layer of mulch as you get closer to the tree, so that it's much thinner nearer the centre, then you don't get that very obvious large gap between the tree trunk and the mulch and it doesn't look like a doughnut.
The best thing you could do is leave that donut of mulch alone. Thrilled you pulled it away from the base of your tree. Now, there are ideas you could entertain to be able to make a human space near a tree or inside a group of trees.
Leaving the mulch donut alone, create an area that juts off to the side of that donut. Using upside down paint draw the dimensions of either a round space, a curvy space, a rectangular space. (Assuming these trees are in a lawn). Dig out the lawn, then down another 2 inches, smooth, level then lay landscape fabric down. The area should be big enough for 2 chairs and a tiny table; about 4'X6'. Ideally edging that space with pressure treated 2X4's held with stakes, the tops leveled, then install the fabric and then install 4" deep crushed gravel. Either way install 3/8 minus which is finer in texture than normal driveway gravel (5/8 minus). Pea gravel is fun but not as stable as compactable crushed gravel.
Place your weather proof chairs and a tiny table. Then add a grouping of similar pots; a big one and two smaller. Possibly a medium sized one on the other end of this informal 'patio'. You can also raise a small plant on top of an upside down pot. A vertical plant, for the large one such as a tall ornamental grass, or even a tree, a beautiful shrub. Stuff annuals and other perennials in all the rest. Keep the pallet of plants small enough to be able to have all pots with at least something to tie them together in a composition. Look for partial shade plants. Definitely lime potato plant ivy that pops right out of the shade. Even variegated leaves the white pops out as well even at night. Look for compatibility among the plants for water, shade, partial shade, pH of soil to help choose your groups. Impatiens will be a huge color producer as well as begonia. Just a couple of ideas...
Use ONLY potting soil. No rocks at the bottom of the soil.
Planting annuals within this donut would be okay. Won't hurt the tree so much as the annuals relegated to a thin layer of soil. This other informal patio, sounds daunting but it really is not. Send a picture of the area you'd like to add some color to.