A very simply dressed green salad and the best bread you can find. Let the crab be the star. You don't want to overwhelm its delicate flavor.

I'm thinking some kind of salad that incorporates bitter greens and citrus to balance out the richness of the crab.

If you're grilling, don't miss the opportunity to grill some corn on the cob to go with the crab legs!

Ditto on the cole slaw (my first thought). Horesradish sauce made with creme fraiche or sour cream. Possibly rice pilaf or quinoa. I'm also thinking a homemade romesco sauce would also go really well with grilled crab legs. Throw some scallions on the grill while you are at...

Old fashioned creamy cole slaw with shredded carrots, mayo, sugar, cider vinegar.
Boiled or steamed skin-on Yukon gold potatoes cut in 1" pieces with lemon butter and parsley.

Grilled asparagus and a salad with avocado and citrus. Sourdough bread.

clam chowder and hush puppies!