Ooh, hope I'm not weighing in too late here.
Okay, DEFINITELY do not miss Capri. The scenery's
fantastic, and next to the Grotto Azzuro is Ristorante Addo Ricco -
when they say the Frutti Di Mare is their speciality, they're not
kidding:

and this is the view from your table:

Bikini girls come as standard equipment.
In Rome, St Peter's Basilica is a no-brainer, but head straight
for the Sistine Chapel first because it closes early. The
Pantheon and Trevi Fountain are nice, and the Spanish steps are
good for hanging out. As for the Colosseum, ehh, take it or
leave it.
Venice is great for just wandering around. If you're at
Piazza San Marco, go up the bell tower - the view's pretty
good:

Note two things, though:
1) You'll need to check you bag in before going up
2) The bell still works, and once every hour you'll find out how
well it works
While you're in Venice, it's worth popping over to Murano on the
water bus to check out their glass-blowing demonstrations.
Speaking of buses, if you're coming in from the airport, the
last time I checked, a boat trip in will cost you 95 Euros, and a
bus trip will cost you 10 Euros. Do the math.
OK, as for Paris, going down the Champs Elysees in the
evening is a must-do, probably best heading towards the Arc de
Triomphe from the La Defence direction. If you want to go up
the Eiffel Tower, it's best to book lunch at 58 Tour Eiffel
(Altitude 95 in old money) because you'll get to skip the queue and
go right up.
If you want to go to Notre Dame, get there early - the queue to
go up to the top fills up pretty damn quickly. It's not so
bad for the Catacombs, although you shouldn't drag your feet there
either. The Pompidou Centre looks cool, but you'll really
have to try your luck to see what they happen to be displaying at
the time. Not a big fan of the Lourve - skipped queueing up
to see the Mona Lisa and I don't feel any poorer for it. Take
a few hours to stop at a classic cafe (maybe near Sacre
Coeur/Moulin Rogue), have a coffee or ten and just watch everyone
go by.
Anyway, that's just a few random thoughts off the top of my
head. Will post more if I think of anything.