Paris in July and August is less busy than usual as many of the resident go in vacation. So if you hear that Paris is busier in summer it is wrong, only the tourist attraction are but the tourist attraction are not the city of Paris.
About the hotel fares, July and August are off season as the number of business travelers drops in summer.
As a resident of Paris, I cannot help you about the hotel.
The cheap eat, it depend where you want to eat because Central Paris is quite big and full of restaurant an other thing.
Look at the price (there are always indicated in the front of the restaurant) and avoid the touristy districts unless you want to eat in a fast food.
I cannot advise you about any restaurant unless you want to eat japanese food (good ramen restaurants Rue Saint Anne in the 1st/2nd arrondissements, metro station Pyramides, it is pretty much the only place where I eat outside my house or a sandwich)
Don't believe what guide siad the 7th arrondissement or Montmartre are not all representative of the real parisian life.
Avoid la Defense on sunday while it is more busier than before with the opening of the mall, it is still better to go here on weekday on the luch time.
The most inexpensive activity in Paris is walking, any place in the inner city is walkable with many shops and etc..
So the best way to visit Paris is to put your fingers randomly on the map and going to this place.