Most points of interest on this itinerary are within walking distance of each other. Uber or Lyft can be convenient for some evening activities. LA is well connected with public transportation so a day pass considering the time plan would be around $8 per person.
To add more to your list, try visiting the Greystone Mansion, a historic mansion with beautiful grounds, yacht ride along the coast enjoying the sunset, or Beverly Gardens Park. For less time, consider skipping the spa treatment or museum visit, and opt for a shorter lunch or dinner reservation.
The nearest airport to Beverly Hills is Los Angeles International Airport (LAX), located approximately 11 miles from the city center.