Just a few days after providing free rides to SXSW attendees in Austin, ride-sharing startup SideCar is announcing plans to continue expansion into new markets. The company, which previously launched in a number of major cities throughout the U.S., is moving east — making ride shares available in Boston, Chicago, and Brooklyn, NY. SideCar operates a service that connects passengers looking for a ride with drivers who have a car and some spare time on their hands. The whole thing is orchestrated through mobile apps that try to find the nearest available driver and sends them to pick a passenger up. Those passengers then pay a “donation” for the ride. It’s been a whirlwind couple of months for SideCar, which launched in San Francisco last summer and expanded to Seattle in the fall.