You always have 5 options on your turn, regardless of where you are 1. Move to a new location 2. Take the quest action for whatever quest you are on 3. Play a special white card 4. Play 3 of a kind to heal 1 life 5. Make an accusation
The only thing that changes based on your location is the quest action available to you.
Furthermore, I'll point out that you are always on a quest. Camelot is a quest, so there's no way in the base game for a loyal knight to not be on a quest. (The Traitor can be not on a quest by being revealed through accusation or the Fate card.)