7 days messing around in Mediterranean cities is a very, very familiar scenario to just about anyone in the UK, I think. My list's therefore fairly similar to Blackhood's, although I prefer taking linen separates instead of his linen suit, and I don't wear shorts. I do take a pair of swimming trunks though, as you might want a dip in a hotel pool for instance. In addition, I take a small suitcase to check-in onto the flight as I prefer to avoid the need to trust hotel laundries, so in reality I pack more pairs of trousers, shirts, polos, shoes & sundries than listed below.
But for the purposes playing along with his carry-on only restriction, and assuming use of the hotel laundry:
- off-white linen jacket
- brown linen trousers
- white OCBD
- chestnut loafers and brown belt
- panama hat
- as for a watch, I take a quartz Seamaster on a metal bracelet. Perfect for travel, as you don't worry about it getting knocked about or anything.
- 2 x linen or cotton trousers (stone, tan, or another colour depending on mood)
- 1 x brightly-coloured linen shirt (e.g. pink or fuschia)
- 2 x normal-coloured cotton or linen shirts (white, pale blue, blue stripes, etc, and at least one has a normal collar in case I need to wear a tie one night)
- 3 x polos (sunny but not crazy colours)
- casual-ish but sober tie just in case
- white cotton hankies
- swimming trunks
- suede shoes of some kind, possibly chukkas if I'm going anywhere near the countryside. If I'm taking chukkas, I'll wear them on the plane and pack the loafers.
- usual other sundries
If that still doesn't fit in the carry-on (as I say, I usually take a suitcase, so it's difficult for me to judge carry-on only wardrobes), then ditch the bright shirt and one of the polos, then if needed one of the pairs of trousers, and make even more use of the hotel laundry.