I would do an apartment. At your price range, you can book a really nice one, cheaper than a hotel for 7 days. Look at VRBO.COM for a start. The ones listed above will also work. Just look and compare prices and get a map and check locations. The closer to the center of Paris, the better, to a point. The bad thing about staying to close to the attractions is the restaurant bills go up and the service/food becomes . . . . .at times. When we are in Paris, we try to eat away from the center of town. A stroll down Avenue de St. Ouen, for example, brings you to a myriad of restaurants, with prices for lunch ranging 8 to 15 Euro for a 3 course meal. Closer in, around tourist spots, the same meal, would be 15 to 35 Euro.
Also, with the roasted chickens, prepared potatoes, cheese shops, wine shops, boulangers, desert shops, Picard frozen veges and other foods,, fresh fruits and vegie shops, available on the street, it is a wonderful experience to walk down the street and buy dinner to be taken back and eaten in your apt. All you have to cook is the fresh vegetables and you are ready to eat like a local.
You will have a lot more room, and more privacy in an apt. No maids coming in and out, some apts have no neighbors, etc. You will be living like a local. We had an apt. last year and really loved it. It was also much cheaper than a hotel, even cheaper than our tried and true Etap on Rue Dr. Babinski. We stayed 2 weeks for almost the same price as one week at Etap. It was worth every penny saved.