I would definitely go for Sorrento and the Amalfi Coast.
Beautiful area with lovely scenery and the most amazing sunsets.
Places to see with a touch of culture are Pompei,Herculaneum and the museum at Naples.
Island of Capri for a romantic day out and the Amalfi Drive for sheer terror.
This area has everything for all ages.
Italy as a whole is a beautiful country and you can't go wrong wherever you go.
Congratulations.

My first reaction was the same!
Sorrento and the Amalfi Coast.
That's where we went on honeymoon and it was perfect..... we're going back this year for our 12th anniversary and we simply can't wait! You can also do a weekend in Rome tour ----------superb!

We've also been to Lake Garda and the Northern End, Riva del Garda and Limone are beautiful as well - loads to see - plus Verona and in reach of Venice. (We've been 3 times)

Have also been to Lido and hated it - the only place we've been to in Italy and disliked --- not very romantic really and more touristy than the real Italy - its nowhere near the Amalfi coast.

The weather is more reliable in the South though if you want guaranteed chill out / relax time Sorrento is your best bit!

I will always come on and defend Lido ....

It ISNT old Italy, never will be, as it was custom built as a resort - but it is a great base for exploring the surrounding area, Venice, the venetian islands, Verona, and even Garda. Also, as you seem to want a beach holiday, Lido has a fantastic beach, and you will more than likely get a private area with your hotel, as that is how the beach is allocated over there (some pics of the areas on my personal website if you have time to look!)

There, my tuppence worth!