This appears to be an option:
DateFormat justDay = new SimpleDateFormat("yyyyMMdd");
Date thisMorningMidnight = justDay.parse(justDay.format(new Date()));
to add a day to it, either
Date tomorrow = new Date(thisMorningMidnight.getTime() + 24 * 60 * 60 * 1000);
or
Calendar c = Calendar.getInstance();
c.setTime(thisMorningMidnight);
c.add(Calendar.DATE, 1);
Date tomorrowFromCalendar = c.getTime();
I have a hunch the latter is preferred in case of something weird like daylight savings causing adding 24 hours to not be enough (see https://stackoverflow.com/a/4336131/32453 and its other answers).