I would stay away from Varadero and surrounding areas ... unless you like a 'cheaper' version of Marbella or Torremolinos, if you know what I mean!
In Havana, you should stay in either the Hotel Nacional or Inglaterra. Beautiful examples of colonial era architecture. If there are out of budget, then choose the Habana Libre, if that is also out of budget ... go camping.
The beaches in the east of Havana are as good as any others on the island.
You much see Pinar del Rio for the tobacco plantations and very special countryside, Trinidad, and maybe even Santiago de Cuba.
Eat at the "paladeros" or at the hotel, avoid tourist restaurants.
Hire a car and just drive around.
Good luck.