For Really Good cheap restaurants, if you like japanese food (not just sushis), you can go next to the Opera, rue Sainte Anne, where there are many good restaurants of that kind.
For French food, next to Rue de la Roquette, there is a restaurant called "Les Galopins" which will serve you very good quality plates, as well as good wines, for very reasonable prices regarding the quality (about 30€/person for a full meal in the evening, including wines and digestives).
On NO account go anywhere next to the Latin Corner for a restaurant, most of them are overpriced, understaffed, and poorly led. (about only tourists get to eat there, did the mistake once, will never do it again)
For the cheaps bars, it all depends on your music style :
- If you like Metal, Rock and the like, go to "La Frange" which is located Rue de Sofia, next to the "Barbesse Rochecouard" metro station. Beware though, the neighboroud is not very tourists friendly, but should pose no problem. (opening time 6pm-2am every day). Cheap, nice, and welcoming.
- Slightly more expensive and surrounded by lots of bars in rue de la Roquette is "Les Furieux" (the furious), one of the most successfull metal bar in Paris (as well as one of the longest lasting)
If you like jazz, to listen to it and to dance to it, you can go to "Le Caveau de la Huchette" which, for a little entrance price, will provide you with that.
As for karaoke, I'm afraid that I'm at loss, but any search motor should see to this. There are little karaoke bars in Paris... It's just not in the culture. Someone once tried to open one like in Korea or Japan, but it failed.
As for the cheap sights... So many of them
- Eiffel Tower (as long as you don't go high)
- Avenue des Champs Elysées (if you resist the shopping tentations)
- Montmartre (the highest point of Paris, for beautiful pictures, and totally free)
- The Parc Monceau (15 min walking distance from the Champs Elysées), for persons with druidic likings
- Beaubourg (the museum itself is quite interesting to see, next to Chatelet's Metro Station) which is dedicated to Modren art. I personnaly loathe it, but the building is nice.
- For a fair price too you can make a tour on Paris' river, la Seine on a boat.
Not to quote the listless museums, cathedrals and such you only can see by walking around and keeping your eyes peeled.
Enjoy your stay in Paris, if you are interested by further or more specific informations, you can contact me.