While I love chicken salad with grapes or celery I also like to make a really basic one where the chicken really shines. It seems so simplistic that it's boring, but really, it's the one my kids and my nieces beg me to make.
I like to throw a couple of extra boneless skinless chicken thighs and breasts on the grill to set aside for chicken salad simply seasoned with garlic salt (Costco has a great blend in a grinder - big pieces of dried garlic and coarse salt) and pepper. If I want a jazzier salad I use one of the rubs we have around and then grill. The chicken can be made into salad later in the week or put in the freezer for later.
Or, if I'm doing an olive oil and rosemary roasted chicken I get a really big one to use the left-overs for chicken salad. In either case I really like to use a blend of white and dark meat - gives it better flavor.
I cut the pieces very chunky, then keep the salad super simple - some yummy diced red onions, slice some canned black olives and just add enough mayo to hold it together, little salt and pepper. If I have used a rub on grilled pieces then I sprinkle a little of the rub in as I mix it up too.
I've used this on pieces of crunchy bread as appetizers at parties - also good on sourdough or pumpernickel bread - YUM!