You could just leave it bare. Cultivate it a few times a year and that will keep the weeds down. Especially if they're maples, nothing much will grow in that dry shade.

Not sure what you mean by large rocks but I've also seen fist-sized river rocks used. Sometimes weeds grow in between. You could put landscape fabric under the rocks.

In some parts of the country, wood mulch either has ticks that come in it or attracts ticks, not sure which.

do you have a source for the ticks claim? I've been doing this over 20 years and this is the first I've heard it.

Mexican beach pebbles / rocks is what I use. I put a weed barrier fabric underneath to prevent weeds growing through it.

Yup, largish rocks (hand size flat ones) on top of landscape fabric. Or get rid of the dog...

I would never get rid of my dogs, they are part of my family. As far as the ticks go, it might be the part of the country I live in, but I have lived in the northeast as well as the southwest, and have had problems. It is probably more a function of the attraction to wood ticks than the ticks being in the mulch to begin with.