Rome, Coast to Sperlonga & Amalfi Coast Trip

Hi

I am taking a 5 night trip to Italy in a few weeks with my husband and
plan the following:

Day 1 - arrive/get to hotel on the outskirts of Rome
Day 2 - Rome
Day 3 - head to the coast and travel down the coast to hotel at
Sperlonga
Day 4 - drive as far down the Amalfi coast and back as we can
Day 5 - leisure in or around Sperlonga

In Rome I want to see the Colleseum and the Trevi fountain - they are
my must sees. Although we only have a day, it will be a long day and
I'd like to think we'll see more than those two things. I wondered if
people had any "hidden gems" - quaint streets, pretty sights, not
necesarily tourist sights, in fact, quite the opposite. I love
photography - of people, places etc if that helps, i.e. I'm not
particularly interested in museums and art galleries.

And the same question for days 3, 4 and 5 really - what are the "must
sees" or your favourite things to see that are not even tourist
attractions.

Thanks very much in anticipation!

Lynda