Cartagena or Medellin
Best option is to fly out from Bogota to either city.
Eje Cafetero (Pereira) or Santa Marta
These cities are a little less known (and less expensive). Pereira is one of the main cities in Colombia's coffee region. If you visit, go to beautiful nearby towns like Salento and Finlandia, and visit Valle del Cocora. Santa Marta is important for it's rich geographical and historical influence. Visit Parque Tayrona for beautiful beaches and archeological sites.
Villa de Leyva or other towns in Boyaca
Villla de Leyva is located 4 hours away from Bogota by car, this is a beautiful town with colonial architecture. It is a good place to spend a weekend in the mountains. For a weekend getaway in a natural setting consider a place like Embalse de Chivor. Also a few hours away from Bogota. Let us know if you need to coordinate transportation for these or other nearby trips.