While concrete curbing around a flower bed or a fence provides an attractive and useful barrier in the landscape, it can also be problematic to trim the grass around it. Lawnmowers can't mow right up against the curbing or fence, and string trimmers may cause damage to the curbing or fence materials. Fortunately, there are some landscaping options that will solve this problem and still look good.
Option #1: Brick mowing strip
Although somewhat time consuming to install, a brick mowing strip installed next to the curbing or under a fence can solve all your difficulties. The process is simple. Dig out the soil in a strip right up against the curbing or beneath the fence. The depth should be about two times the thickness of the bricks you are using. Line this trench with landscape fabric to block weeds, and then fill it half full with sand. Set each brick into the sand, leveling them as you go, and then fill in the joints between the bricks with more sand. Now grass can't go right against the fence or curbing, so you don't have to worry about trying to mow too closely to it.
Option #2: Gravel no-man's zone
You can achieve a similar strip using gravel instead of bricks. Simply skip the sand and place the decorative gravel right on top of the landscape fabric. Gravel isn't as durable as bricks, though. You should avoid mowing over it directly, since the lawnmower wheels can get stuck in the gravel or pull it out into the grass. Instead, gravel provides a buffer so you can use a string trimmer without hitting the fence or the curbing. Just make sure it extends out far enough so the trimming strings don't still reach the fencing.
Option #3: Plant protection
Sometimes the best buffer is a living one. Low growing ground covers, like creeping thyme, can be planted in a strip along the perimeter of the curbing or fence. This way you have green coverage but you don't have to mow too closely to the fence or curbing and worry about mechanical damage. If the lawnmower or trimmer catches a little bit of the groundcovers edges, it's not a big deal because it grows back. For tall privacy fences you can even go beyond groundcover and plant low shrubs, such as lingustrum.
For more help in landscaping and maintenance around difficult areas, talk to a landscape maintenance company, such as Show-Me Mowing in your area.