I love Paris, my sis lived on the outskirts for a few years so often went to visit ( she also lived on the Cote D'Azur for a while as well. now unfortunately she has settled in Brittany....

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Use the public transport, its the only real way to get around. Walking is good as well but can be knackering! get a pass for the metro, similar to london it works on zones and you can also jump on buses with it. saves messing about with tickets here there and everywhere.
The Mona Lisa is tiny and usually surrounded by japanese!
when eating in restaurants either stick to the daily special menu ( fixed price) or even better go down to teh Latin quarter ( near Notre Dame) and go a few streets back from teh River. This is a student area so food is dead cheap but still really good on teh whole.
be aware of different prices to sit outside and inside.... sometimes its significantly higher!!!
If taking teh missus (not sure if you have a significant other) get some cheeses, french bread, grapes, saucisson etc and a bottle of pink bubbly and sit near the tower for a picnic.... cost ~ 10 quid, brownie points - priceless!!!!! ( Mine still mentions that picnic 10 years on.... )
Also, take your camera as you will see loads of 'nice' different old cars like DS's renault 4's facel vegas and the like. usually they are bashed and battered from life on teh streets but it always makes me smile when I see something a bit different being used
a ride on teh Bateaux Mouche is a good way to see teh city especially at night when its all lit up but watch for gobby merkins. I nearly ended up planting one whilst I was Queuing........
BTW, watch it if you decide to go to Sacre Coeur. where you get off teh metro is a BIG pickpocket and Red light area........... if you go round teh back there is a famous square where artists will paint your piccy and just further back is Jim Morrisons grave.