The ideal level of doneness for a ribeye steak depends on personal preference, but it's commonly recommended to order a ribeye steak at either medium-rare or medium doneness to fully appreciate its flavor and tenderness.

Here's a breakdown of different doneness levels for ribeye steak:

1. **Rare**: The steak will have a cool red center and be very soft to the touch. It will be cooked quickly on the outside and mostly raw on the inside.

2. **Medium-Rare**: This is a popular choice for ribeye steak. The steak will have a warm red center and be slightly firmer to the touch. It will be pinkish-red throughout with a hint of brown on the outside.

3. **Medium**: The steak will have a warm pink center with a bit of juice visible. It will be firmer to the touch compared to medium-rare and have more brown coloring on the outside.

4. **Medium-Well**: The steak will have a slightly pink center with minimal juice visible. It will be firm to the touch and have more brown coloring throughout.

5. **Well-Done**: The steak will have no pinkness and be fully cooked through. It will be firm to the touch and brown throughout, with little to no moisture visible.

For ribeye steak, many people prefer medium-rare or medium doneness to fully enjoy the tenderness and rich flavor of the meat. However, the best doneness level ultimately depends on individual taste preferences. It's essential to communicate your desired level of doneness clearly to the server when ordering at a restaurant to ensure that your steak is cooked to your liking.