Plan for a day hike near your home the same way you would plan for a day hike anywhere: research the trail, find out whether you need a permit, check the weather, set an itinerary and decide what to take with you. Make sure to leave your itinerary with someone in case of an emergency.
Find out whether the trail you wish to hike is suitable for your ability. If it is considered advanced and you are a beginner, you may want to choose another trail. Calculate how long the hike will take based on whether the terrain is steep enough to require a lot of climbing and on your fitness level. Note major landmarks along the trail to make sure you're staying on the right path. Find out where you can get water. Select places along the trail to stop for lunch and rest breaks, and plan when to turn around and head back.
Check whether the park or wilderness area your trail is in requires a back-country permit. It may be free. Not having one may cost you a fine if a ranger asks for it. Checking with a ranger before the hike is also a good way to find out about any recent changes to the trail, such as mudslides or downed trees.
Decide what to pack based on your itinerary and the weather forecast. You may dress for a hot day, but take a jacket or rain poncho in case the weather changes. Some things to bring along include trail maps, a compass, water, lunch and snacks, a first aid kit and any special gear needed for your route. Balance your choices against the fact that taking more will weigh you down more.