www.parisattitude.com, you will find many suitable apartments, villas for rent in this website. Some are real cheap, with kitchen and all the facilities.

Transportation... Bus/ Metro are economical (you can get a pass for a week, available at all Metro stations) and you can get a cycle too.

Stay somewhere near Tracodero... Which is near the Tower Eiffel, metro is connected to all the places you have to see in paris.

Paris night life is wonderful, plently of places to eat and drink.