Day 1 — Downtown Dubai
Burj Khalifa (book the observation deck slot in advance), Dubai Mall, and the Dubai Fountain show in the evening. This area is walkable once you're there, making it a low-effort first day after travel.
Day 2 — Old Dubai and the Desert
Morning in the Al Fahidi historic district and a short abra (traditional boat) crossing over Dubai Creek to the gold and spice souks, followed by an afternoon or evening desert safari to contrast the city with the desert.
Day 3 — Beach and Palm Jumeirah
A relaxed day around Jumeirah Beach or a beach club, with an afternoon or evening at Palm Jumeirah for views of the Atlantis resort and The Pointe waterfront.
This covers Dubai's essentials without over-scheduling — if you have a 4th day, add Dubai Marina and JBR Walk, or a day trip to Abu Dhabi.