My biggest piece of advice is to wander. Seriously. Take the Metro, go to an interesting neighborhood and get lost for the day; go into the supermarket, pay attention on the train. You absorb so much just by being there and being around people. I'd also suggest trying to focus on three or four cities you really want to see rather than trying to see everywhere; you'll get a lot more out of it.
Specifically, for the cities you've mentioned: London has so much to see and do that it would take pages and pages. Best museums: National Gallery, British Museum, British Library, Wallace Collection. Tower of London is touristy, but fascinating, so don't miss it. Go to Speakers' Corner or try to get a seat at Question Time. If you're anywhere near Dover or want to take a trip, they have the Roman Painted House, the ruins of a Roman tavern/hotel with central heating. It's incredibly cool.
Paris: If you're going to be there for a few days and want to hit the museums, get the Museum Card. Best museums: Musee d'Orsay, Musee du Moyen-Age; Musee Rodin, the sewers (trace Jean Valjean's route), the Catacombs, Sainte-Chapelle. The Arenes de Lutece in the 5eme is a Roman arena that is now a park, and is a great place to have a picnic. If you go to Notre-Dame, make sure you climb the towers.
Also, if it's on the way, consider stopping in Lyon. It's IMHO a much more enjoyable and nicer city than Paris and has fascinating things to see and do.
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Specifically, for the cities you've mentioned: London has so much to see and do that it would take pages and pages. Best museums: National Gallery, British Museum, British Library, Wallace Collection. Tower of London is touristy, but fascinating, so don't miss it. Go to Speakers' Corner or try to get a seat at Question Time. If you're anywhere near Dover or want to take a trip, they have the Roman Painted House, the ruins of a Roman tavern/hotel with central heating. It's incredibly cool.
Paris: If you're going to be there for a few days and want to hit the museums, get the Museum Card. Best museums: Musee d'Orsay, Musee du Moyen-Age; Musee Rodin, the sewers (trace Jean Valjean's route), the Catacombs, Sainte-Chapelle. The Arenes de Lutece in the 5eme is a Roman arena that is now a park, and is a great place to have a picnic. If you go to Notre-Dame, make sure you climb the towers.
Also, if it's on the way, consider stopping in Lyon. It's IMHO a much more enjoyable and nicer city than Paris and has fascinating things to see and do.