Calendar and Date

Calendar.getInstance() gives you a Calendar object representing the current date. You can then add to this using calendar.add(Calendar.DAY_OF_MONTH,1), and it will handle the wrapping onto the next month and the next year itself.

Calendar doesn't have a good String representation, but there is a class called SimpleNumberFormat that can format Dates as Strings. Calendar can give a version of itself as a Date, using calendar.getTime(), so we get the following:
formatter.format(calendar.getTime());

Here is a code example that uses this to set up a JComboBox with an entry for every day in the coming week.

import java.awt.FlowLayout;
import java.util.Calendar;
import java.util.Date;
import java.text.SimpleDateFormat;

import javax.swing.JComboBox;
import javax.swing.JFrame;

class Main
{
	public static void main(String[] args)
	{
		Calendar calendar=Calendar.getInstance();
		JFrame frame=new JFrame();
		frame.setLayout(new FlowLayout());
		frame.setSize(400,400);
		JComboBox box=new JComboBox();

		SimpleDateFormat format=
			new SimpleDateFormat("EEEE, d MMM yyyy");
		
		for (int a=0;a<6;a++)
		{
			calendar.add(Calendar.DAY_OF_MONTH,1);
			box.addItem(format.format(calendar.getTime()));
		}

		frame.add(box);
		frame.setVisible(true);
	}
}

These are the API docs that are relevant here: Calendar, SimpleDateFormat and JComboBox.