Split your stay, but weight it towards the beach, and here is the reasoning.

Stone Town is genuinely worth one to two nights. It is a UNESCO World Heritage site, and wandering its narrow streets, visiting the old fort, the spice markets and the historic doors, is best done unhurried rather than as a rushed day trip squeezed in on your way somewhere else. Staying overnight also lets you experience it in the cooler evening hours when the atmosphere shifts and it is genuinely pleasant to walk around, rather than only seeing it in the midday heat.

The beach areas, particularly the east coast around Paje, Jambiani and Bwejuu, or the northern tip around Nungwi and Kendwa, are where most people spend the bulk of their trip, and reasonably so. This is where the powder sand, turquoise water and relaxed pace that Zanzibar is known for actually live.

For a typical week-long trip, one to two nights in Stone Town at the start or end, then the remaining time at a beach base, works well logistically. Stone Town sits close to the airport, so bookending your trip there rather than in the middle avoids unnecessary transfers.

If your time is genuinely tight, under five days total, a single day trip into Stone Town from a beach base is workable, since it is roughly an hour to ninety minutes from most beach areas depending on which coast you are on, though you lose the evening atmosphere that makes an overnight stay worthwhile.