I’ve been to Paris twice and love it. Eating and drinking out is VERY expensive: think 6-7 euros for a beer or glass of wine, 8-10 euros for a cocktail or small glass of champagne, and anything upwards of 20 euros for a very simple evening meal. If you have kitchen facilities, shop at the superamrket and have breakfast and lunch at the apartment/take packed lunches out with you to save money. I’d also recommend buying drinks/water at the supermarket; you can pay about 2-3 euros for a bottle of water or can of coke, wherea syou can buy 6 bottles of water for 1-2 euros at the supermarket.
In terms of sightseeing, loads of attractions are free, or very cheap. My top picks are:
The Sacre Coeur. It is utterly beautiful and the views are amazing. If you have a metro pass, you can take the funicular up the hill for free (NB: definitely invest in a travel pass; we paid 14 euros for a 2 day pass and it is WELL worth the money, it gets you unlimited access to the metro, buses, etc); otherwise, there are a LOT of steps to clim to get up tp it! There is a small charge to clim to the top (a couple of euros when we were there in September 2009)
The Eiffel Tour: prices vary depending on whether you take the lift or stairs; I think it’s approx 15 euros pp if you take the lift. It’s a ‘must do’ though IMPO
Seine River cruise: we paid about 8 euros pp, and it goes up and back down the river with a commentary on all the sights; great way to see Paris and learn some interesting facts. The one we took departed from next to the Eiffel Tower.
Champs Elysee and the Arc du Trimophe. I haven’t been to the top of the Arc du Triomphe, but again entrance is minimal. Another ‘must see’.
Food market: we went to one an approx 10 minute walk from the Eiffel Tower. The food is AMAZING, and we bought things for a picnic inc beautiful cheeses, flans, cakes, breads, pate, and fruit. It was all delicious and is definitely worth a visit.
Notre Dame Cathedral: free entrance, small charge to climb to the top. Again, you can’t visit Paris without visiting the Notre Dame. The small ‘treasury’ section is worth a look; it costs a few euros but some of the chalices are unbelievable, covered in jewells.
Saint Chapelle: this is near the Notre Dame (approx 5 minute walk). It is a beautiful chapel with huge stained glass windows; well worth a visit. Entrance costs a few euros.
Berthillons ice-cream: this is on the island next to the Notre Dame (I forget the name; I think it’s Ile Saint Louis). The ice cream here is SUBLIME, and the sorbets to die for. The island is also very pretty, with some beautiful old houses and buildings, and lovely shops.
Pompadou centre: pretty cool and again worth a visit. I also enjoyed the Picasso museum.
The Louvre: I still haven’t been here but hear it’s worth a trip. Focus on one section though as it’s massive.
I would recommend investing in a guide book, and planning things out to save you wasting time going back on yourself ie arrange to see things in a similar area in the same day. Also check out the nearest metro stop so you can work out routes in advance; I found this helped as I found the metro system a bit confusing at first. Guide books will also have shopping guides, as obviously Paris has some amazing shopping; you might like to check out Lauduree, for instance, or one of the many choclatiers.
Hope that helps!