Pretty much any district of central Paris has good access to the metro and is safe, really. So that doesn't narrow things down so much. And renting an apt isn't automatically cheaper, of course, it depends on how much you spend on it vs. a hotel. YOu do realize that with an apt. you will have to pay money for a security deposit and likely pay in advance (partially or totally) and not be able to change your dates or get refunds? But 8 nights is a good amount of time, so you could get something cheaper than a hotel if you choose a cheap apartment.

it's hard to know exactly what your budget is and what you want, but it sounds like you are younger (I'm guessing, less than 30?) and so I'll suggest you might look in the 11th arrondisement or the 5th, they are a little cheaper on average than some others in the center. But you could also try the 13th or 12th or 9th-10th.

Central paris should be safe and the Metro is practically everywhere. Take a look at airbnb.com's neighborhood guides in paris - they have good descriptions of each neighborhood and you can find apartments for rent for your specific dates.

Loook at vacation in Paris apts. They do not require s security deposit and you pay in dollars before you leave and have the keys in hand so you are not waiting for someonr to let you in,

Thanks! This was helpful.

Hotel Diana and Hotel Saint Pierre are both super central, and often have rooms under 100 euros, and both have a/c .

Check out the Victoria Palace Hotel in the 6th, just off Rue de Rennes, a street over from Blvd. Montparnesse, 5 minutes from Luxembourg Gardens and 5 minutes to the St. Placide Metro stop. The two bedroom suites are perfect for a family with small children and the hotel is very kid friendly. We had the lavish buffet breakfast included in our rate every morning, a bonus when traveling with little ones.