Lyon, France

The classics:

The old city on the western bank of the Saone, known as "Vieux Lyon", with its mainly renaissance buildings and famous "traboules" (passageways through buildings).

The other old city on the northern Croix-Rousse hill. The nicest non-strenuous way to reach it is by the S6 trolleybus route, with tiny electric buses taking power from overhead wires picking their way through narrow streets.

The Fourviere hill above Vieux Lyon, with fantastic views and the over-the-top basilica.

The old Roman theatre on Fourviere.

More specialist attractions that should be visited if you are interested in the subject:

The Centre for the History of the Resistance and Deportation - Lyon played a famous role in the French Resistance, and this is a very deep though at times very grim exploration of the Resistance and the Holocaust in France.

The Lumiere Museum - featuring the history of the cinema pioneers the Lumiere brothers, and other early still and moving photography.

The Henry Malartre Museum - one of France's best auto museums, partly in an old chateau, at Rochetaillee, a small town a little way north of Lyon on the river Saone (frequent buses from the centre).

To the above, if you like food seriously consider planning your meals in advance. While even the lowest of restaurants seemingly has high standards, you can maximize the experience with a little advance booking. Also, the markets are excellent (although I just so you are going in April, so perhaps the Halles Paul Bocuse will be better of the two big ones, with prepared foods than the fresh outdoor market). Finally, although you will find plenty to do (and eat) in three nights, there are day trips to places like Perouges.

In addition to the list provided by Philip, I'd add the Museum of Fine Arts, the Museum of Contemporary Art and the Textile Museum.

There is a really cool boutique hotel called LE COLLEGE that was made from an old middle school. I plan on staying there next Christmas.

I'd add the Museum of Miniatures in Vieux Lyon: https://www.museeminiatureetcinema.fr/en/. A quirky and fascinating museum.
As to a car, unless you plan on a day trip outside of Lyon to places not served by public transportation, a car is not needed. Public transportation is excellent, and driving and parking in the city is not easy.