We're arriving at either Rome or Genova and looking for affordable, nice, authentic-ish in good location. Aim either to hang out there for a week (parc i pini?) or head off to Tuscany (Parco delle Piscine??) or down to Amalfi to try and pack in Pompeii (easy bed hostel??)
These places sound good and cheap online but am aware that Italy expensive for car hire and eating out so may be wise to stay nearish to start point