Go to Villa Giulia
I have been there during the winter. I do not remember these gardens to be extraordinary, but maybe was this due to the season? They were nice however. Lovely grotto.
This is a great villa in Rome to have a wonder round with the family. There is an entrance fee. However you can spend a good deal of time here for that fee.
The architecture itself is fabulous. The paintings on the ceiling must be looked at. Build for a pope and now available to us all. It is a great few hours experience.
There are a number of things to see and do and you will leave with some great memories and photos. Here is more information and pictures of Villa Giulia