Homer's position at the end of the road and the edge of the bay makes it a natural base for exploring further. The two most important day-trip destinations require a boat. Both are worth doing if the weather cooperates.
Kachemak Bay State Park is the obvious first trip — a water taxi from the Spit marina drops you at a trailhead in 20–45 minutes and picks you up later the same day. The Grewingk Glacier Trail is the most popular; the Saddle Trail offers harder terrain and bigger views. Tide pool beaches at low water are excellent for wildlife.
Halibut Cove is an art community of about 20 residents on an island across the bay, accessible only by the Danny J ferry, which makes a lunch run and an evening run from the Spit in summer. The town has no cars, boardwalks instead of roads, a good restaurant, and several galleries. The evening trip includes dinner; reserve ahead.
Seldovia is a small fishing town further around the bay, quieter and more lived-in than Homer. The Alaska Marine Highway ferry calls here, or water taxis make the run in season. Seldovia has a lovely boardwalk along the slough, a couple of good seafood restaurants, and very few visitors.
For those with a rental car, the Kenai Peninsula is one long potential day trip: Soldotna and Kenai (salmon fishing towns), Seward (Kenai Fjords National Park and Exit Glacier), and Homer's own backcountry above the bluff are all within a few hours. The Sterling Highway back toward Anchorage passes through excellent moose habitat — you are almost certain to see moose if you drive it slowly.