Green Bay sits at the base of the Door Peninsula, one of Wisconsin's most scenic areas, and makes a good base for exploring it. The peninsula extends 70 miles northeast into Lake Michigan, flanked on the west by the bay and on the east by the open lake, with a series of small towns, state parks, orchards, and wineries along both coasts. Sturgeon Bay is the nearest Door County town, about 45 minutes north. Peninsula State Park, near the village of Fish Creek further up the peninsula, is a 3,776-acre park with limestone bluffs, bike trails, and camping.
The Oneida Reservation, immediately west of Green Bay, is worth a half-day visit for its casino complex (if that's your thing), the Oneida Nation Museum, and the community's farm markets.