One useful naked eye project, regardless of the sort of observing you usually do, is to just monitor the conditions of the sky at your location. Keep a weather log and keep track of which days are cloudy and which are clear. Statistics on temperature and humidity might also be interesting. Note the naked eye limiting magnitude. Look both at the zenith and toward the horizon.
Light pollution causes major problems with astronomy.
Light pollution tends to become less of a problem late at night because many lights are shut off at those hours. The Moon is a favorite object for observers of all kinds. Here are some ways you can enjoy the Moon as a naked eye observer. Search for a Very Young or Very Old Moon Search for a very young or very old Moon. If you have a good horizon view to either the east or west, this might be a good project for you.