I'm not sure it is the *first* address of the *first* nic (depends of where you begin to count :) ), but one of your IPs can be found out, for example, this way:
 
 boost::asio::io_service io_service;
 boost::asio::ip::tcp::resolver resolver(io_service);
 boost::asio::ip::tcp::resolver::query query(boost::asio::ip::host_name(), "");
 boost::asio::ip::tcp::resolver::iterator iter = resolver.resolve(query);
 boost::asio::ip::address addr = iter->endpoint().address();
 std::cout << addr.to_string();