Barcelona: 5 Days in Barcelona
I stayed 3 days/4 nights in Barcelona - I felt that was enough. Unsure of how many days you would need in Majorca.
Miami Beach: I have only two days in Miami
Lummus Park Beach
Madrid: Best Places to Eat in Madrid?
Mercado de San Miguel
Las Vegas: Working in Vegas but will have free time
Gordon Ramsay Steak, La Cave Wine and Food Hideaway, Mon Ami Gabi
Barcelona: Area to Stay in Barcelona, Spain
Anywhere close to the main street, La Rambla. Barcelona has an excellent Metro system.