A car is essentially required. Tallahassee has a public bus system (StarMetro) that serves the university corridors and major roads, but coverage is thin and schedules are infrequent outside of weekday rush hours.
The city is compact enough that driving between neighborhoods takes 10–15 minutes. Traffic is manageable most of the time, with predictable congestion on Monroe Street and Apalachee Parkway during the evening rush (5–6 pm). During FSU home football games, the area around Doak Campbell Stadium backs up badly — plan around it or walk from further away.
The St. Marks Trail is the main cycling route south, and the canopy roads are good for driving rather than cycling. Rideshares (Uber and Lyft) are readily available, particularly around the university area.