Heeey, I'm french and I live near Paris.
So, where to start...

WHERE TO DRINK : If you want to go in a pub and don't want to pay a high price, there is "Les Sans Culottes", 27 Rue de Lappe. It's near Bastille subway station. I suggest you "Le dernier bar avant la fin du monde" I just love the whole "geek" atmosphere and if you are lucky, you can see famous people on the videogames/comic/internet universe.

WHERE TO EAT : GO IN A BAKERY AND EAT PASTRIES. I'm addicted to french pastries. They are so delicious and they look so good... I suggest you the Paris-Brest cake, the crème brûlée, the Kouign-amann and the Tarte Tatin.
My friend tells me that at 3 Rue Jules Vallès, there is a restaurant named "Chez Mamy" which is cheap (15euros the menu) and good. My dad also says there are a lot of small and cool restaurants at Rue Monge (subway station : Monge Place). French restaurants are quite expensive, but you can find good restaurants for 20-30 euros. I think It will be the bigger budget in your trip.

WHERE TO GO : Eiffel Tower, Notre-Dame Cathedral, Bastille Place, Le Louvre Museum ,(it's a very good museum), LE MOULIN ROUGE (go go go), and a lot of places... There is a huge historic past in Paris, so I think you should probably looking for what you really want to do.

if you want more informations for restaurants with cheap prices, you can go to the tourism website of paris : en.parisinfo.com/
There are a lot of informations about where eating out, what you have to see, etc... 

So have a nice trip and I hope Paris will be a good time for you !