What zone are you in? Does the space get much sun?

You can incorporate river rock and a large stone to anchor the space. Add one or two grasses - just make sure they don't self seed.

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We are zone 4

It would be helpful to see more the yard to see how this will relate to the rest of the landscape and the house.

Start yourself a rock garden ideabook.

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Here is a plant guide to your zone: https://www.gardenia.net/plants/hardiness-zones/4

Also, some fantastic information about rock gardens: https://www.gardenia.net/gardens/garden-styles/gravel-and-rock-garden

Something to keep in mind- I did a fairly good sized rock garden on a slope. I love it and it is beautiful. It is also the most difficult area in my yard to maintain and I have a lot of yard. While plants are establishing weeds grow and weeds mean hand weeding. Crawling around on rocks and on a slope is very uncomfortable. Very.

My method was to site the rocks used as steps, define the borders, place the large rocks, then plant a very wide variety of deer resistant ground covers and alpine type plants plus a few ground cover type conifers to fill up space quickly. Then I waited to see what did well and bought more of those plants and didn't waste time trying to maintain those that did not like the conditions.

Like I said my area is gorgeous but it is the only place I find myself procrastinating about weeding because there is simply no comfortable way to do it. You're either sitting on rocks or kneeling on rocks and you better have decent balance because it is all on a slope. Tiny weeds poking through ground cover mean having to get in there with your fingers to separate what to pull and what to nurture. Keep this in mind as you do your design.

If you are on the east coast, or anywhere it rains, listen to Cearbhaill. A rock garden is going to be quite a high maintenance proposition because of the weeding involved. If that isn't your thing, a hillside groundcover planting is more what you are looking for.

Why would a rock garden require any more weeding than any other type of garden?

Look at the OP's photo.....this is not a steep slope nor a huge area. Weeding will be minimal once properly cleaned out and planted.

River rock thrown on dirt without landscape fabric or some other similar cover becomes impossible to weed - ask me how I know:) The rock gets imbedded in the soil and the weed roots grow in and around. I had to dig all the river rock out of a small garden area - lesson learned.

Look at some instruction on how to do this - don't just wing it. I just finished a dry creek bed with a very small waterfall. The creek bed is lined with pond liner and only large, but easily movable rocks are along the edge of the liner - on top of mulch because the whole thing is in a garden. River rock is on the pond liner only. To grow plants, you need something that will let water through - so probably landscape fabric - but you also want it to last many years.

A rock garden is not just a bunch of river rock or gravel dumped in top of the soil. Rather it is the careful selection and placement of larger (and a few smaller) rocks to provide context and definition of the planting area and then the rest of the open soil planted with whatever low growing rock garden type plants you prefer. While they share a few similarities, a dry stream bed is not the same as a rock garden :-) Although you can include a dry stream bed as part of a rock garden but it is certainly not a requirement.