Which of the following drugs is primarily used to stimulate urinary and gastrointestinal motility?

Neostigmine is primarily used to stimulate urinary and gastrointestinal motility due to its role as an acetylcholinesterase inhibitor. By inhibiting the enzyme that breaks down acetylcholine, neostigmine increases the levels of acetylcholine available at cholinergic receptors, enhancing the effects of acetylcholine. This leads to increased muscle contractions in both the gastrointestinal tract and the urinary bladder, making it effective in treating conditions such as myasthenia gravis, postoperative ileus, and urinary retention.

Pyridostigmine, while also an acetylcholinesterase inhibitor, is primarily used for myasthenia gravis management. Physostigmine is more commonly associated with reversing anticholinergic toxicity rather than stimulating motility. Donepezil is specifically used for cognitive enhancement in Alzheimer's disease and does not have significant effects on motility. Thus, the primary use of neostigmine in enhancing urinary and gastrointestinal motility makes it the correct answer.