For training purpose I prefer grass for the very same reasons as mentioned before ( less wear on the skids, less noisy etc).If the grass runway is all muddy (e.g. in winter time) or if there are too many molehills than you better do something else that day.
A prepared grass runway should be as solid and as plain as the paved runway with its expansion gaps. Same applies to the shoulder next to the runway.
However you might want to check whether you are allowed to land next to the runway (for training purpose). In some countries you are not allowed to land next to the runway (might be considered off-airport landing) unless it is an emergency.
In real life I would probably aim for the concrete.
Funny CRM story at the end: spent my vacation in the US and thought it might be a good idea to refresh my FAA license and get my biennial done.
During autorotation I was aiming for the grass whereas my very experienced USCG FI got an increase in heart rate and, by softly pushing the stick with his knee to the opposite side, tried to tell me to go for the concrete. We put the a/c down safely on the grass which made him somehow breathe a sigh of relief.
However he asked me to do the next one to the paved runway.
