Be sure to try things from our culture, like going to a fish and chippy! If you want to be a generic tourist, I guess you could visit Big Ben, the Houses of Parliament and go on the London Eye (Also, ride on a red bus, and use a red telephone box). There are some really cool museums all around the place (I particularly like the History museum and the Science museum), and you can get around London using the metro system. Since you are there for 3 days, you could go to London Zoo, or have a picnic in Hyde Park as the weather is quite nice (for British standards) this week. I also recommend going up the shard, but unless you swim in money, I don't suggest eating lunch/ dinner up there. For more British culture, also visit the Camden Market, but some places in Camden are really dodgy.
Paris on the other hand is really dodgy, and from experience there is not a lot to do. I've been quite a few times with family and friends, but sadly is not a good place to spend with family for 3 days. The Louvre and going up the Eiffel Tower is fun, but I don't recommend straying outside Tourist areas.
I've been to Rome twice, and it's an amazing place, there are many restaurants that sell the generic pizza and spaghetti, which is really delicious. The coliseum is a really cool place to visit, it shows the ingenious architecture of the Romans. Also be sure to go to 'Gelato' shops, they sell ice cream, but in at least 30 different flavours ranging from mint to Nutella. I suggest regularly buying fresh water, as summers in Italy and boiling hot, and being dehydrated in the queue to the Coliseum is not fun. Also, one thing, be sure to find fountains in which you can dip your feet in, it's nice and refreshing.
