Hi, if well if you have never been to Italy previously? ROME is a city that you need to visit, there are golf courses but i would mention Golf in Italy is not often cheap so you should have a healthy budget!
I play at donnafugatagolfresort sometimes but it is 150 euro for a round (Italian Open was there two weeks ago) so not exactly budget golf
Realistically unless you are 100% addicted to golf golf golf, a visit from the UK? to Italy is going to be more than just golfing, my favourite place is Sicily, then Rome, which is why i live in Sicily and visit Rome often!
Italy is not a Spain, Portugal or Turkey when it comes to golf, even the 9 holer here costs plenty, but the views are amazing! VIEW OF 9 HOLE COURSE
Where are you from?