For the moment Bercy is no longer skatable but République is the new go-to spot, gare de lyon has also really good spots.
If you want to see some footy to get motivated check
http://liveskateboardmedia.com/fr/parisii and if you see some spot you like don't hesitate to ask to some guys at Nozbone, I'm sure they will help you.
For skateshops you have Nozbone close to Nation (the best all around town), Snowbeach close to Bastille (and close to Charlie Hebdo) and Starcow skate close to Châtelet les Halles.
As for bars there are so much places to go, but the ones on the east side of the city are generally cheaper and more interesting: around Bastille, Le Marais (Gay area but still cool), République, Grand Boulevard have a lot of cool places to go.
If you want to go to concert during august there is generally Rock en Seine, a big festival with big artists from all over the world that can be fun.
http://www.rockenseine.com/If you are going in august be ready to some suffocating weather and high temperatures. August is one of the worst months to stay in paris because most parisian are out of the town and most of the people are tourists. In another hand you will have fun on the boarder of the Seine where you will find some beaches for the summer (but you can't swim).
While you are here be sure to hit the Louvre, Picasso Museum and Pompidou museum (contemporary art).
As said by HATE, Airbnb is the best option for a short period of time in Paris right now.
practice saying 'merci' and As HATE said french people appreciate it when you make an effort to speak in their language, so try to learn some basic stuff.
Parisian people can be really close-minded people (I lived there for 20 years) so try to be polite and speak a couple of words.