WARNING: I'm a gardening novice so please forgive any stupidity.

So there is a small stream that runs through my property all year long (fed by an old mine shaft). This stream is usually lined with all sorts of ugly, fast growing weeds. I recently burned away all the weeds and put down grass seed with decent success. But I am now wondering if there is any sort of weed/vine type thing that I could introduce to this area that will dominate the other weeds while not growing super tall/fast. If anything like that exists, what could it be? Obviously weeds that are mildly aesthetically pleasing would be preferred (if those exist). It wouldn't be a problem for me to burn or roundup everything that's there now to give the new plant a head start, but basically I'm looking for a plant that will become a uniform ground covering plant along my stream where it is too steep to mow and weed eating sucks.