Beef shoulder is commonly referred to as chuck. The consistency of chuck is fibrous but flavorful due to a high amount of intramuscular fat. Deciding what to substitute in place of shoulder meat depends entirely on the cooking method you intend on using.
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Chuck braises extremely well, especially when shredded or cubed in stews. If you intend to shred it, another fibrous cut that braises well is brisket. If you are cubing the beef for a stew, bottom or top round is flavorful and holds up well to long braising. Braised short ribs are another good substitution.
Chuck makes a decent roast with potatoes, onions, carrots and celery. However a substitute that could even surpass a chuck roast would be a rib roast. Rib roasts generally cost much more than chuck. A more cost-effective substitution could be a sirloin tip or top-sirloin roast. These will be leaner than chuck, so a liberal coating of oil before roasting can help to keep the meat flavorful.
There are few cuts from the shoulder that are good steaks for grilling, but substitutions for grilling are numerous. Rib eye or rib steaks will be more expensive, but more flavorful and tender. Skirt steak and flank steak will match the consistency of chuck eye steaks, but flank steak can be more tender if sliced against the grain of the meat.