A week would be just enough time to do a trek to Machu Picchu.
The Inca Trail and KM104 both require permits that need to be booked in advance. You can look into it for April but they're just about entirely sold out at this point.
Alternatively you can look into the Lares or Salkantay treks, neither of which require permits but you should do the right amount of research to secure good guides.
If you're super budget conscious you can take buses and shared taxis from Cuzco to the hydroelectric station then walk the rest of the way.