What kind of sites are you talking about? Because a week isn't a whole lot of time, and there's plenty to see within Paris, which can be crossed on foot from one end to the other in under an hour :-). That said, all of what's considered 'suburbs' is easily accessible by train (metro if nearby, RER if further, like to the airports, and finally 'trains de banlieue' from all the major train stations). If you're American only New York can begin to compare in terms of frequency and accessibility. Unless your tastes in sites is very esoteric, I'd prescribe a whole lot of walking interspersed with a few train trips. Walking through Paris is worth any site imho..
There are a few things to supplement though. The RATP is your main metro/bus resource for in town/close suburbs transportation. Check out the 'forfaits' which are illimited passes https://www.ratp.fr/en/visite-paris/english/preparing-your-trip-tickets-and-travel-passes-designed-you
And another thing is that if the wind in your face is important, Paris is stuffed with bike rental stations. You can use your regular credit card right at any of the hundreds of stations to buy a pass ranging from one day to a year. It's cheap, it's fun, it's very practical (but don't expect to get a bike at the top of Montmartre..). http://en.velib.paris.fr/
Traffic in Paris is scary. Motorized 2-wheel vehicles have a death rate 150 times that of cars. But it's better for bikes. And both cars and pedestrians are much more used to bikes than in the US. So if you're careful, and used to traffic as not-a-car, I wouldn't entirely advise against biking.