If you ever want to truly experience real life time travel, visit Havana as soon as you can. The moment we landed I felt immersed in old world glamour amidst a crumbling, yet beautiful city. A lot of people will recommend going outside Havana, but be aware it will be very underdeveloped and for a weekend you certainly have more than enough to do in Havana. Airbnb is definitely the most worthwhile choice, as the hotels really aren't worth the money. Make sure to bring enough cash to last your entire trip as credit cards aren't accepted.
My favorite spots were O'Reilly, El del Frente, La Guarida, Otramanera and El Dandy. Make sure to walk around Chinatown and the university for a more local feel than old town Havana. Take a vintage care around town, but don't forget to bargain for your money's worth.