This apartment is SO amazing. Small, but not claustrophobic. Beautifully decorated and cozy, a full kitchen, a nice balcony (although the main view is of the building across the street) from which you can see The Saone river, a nicely renovated bathroom, and a comfortable bedroom that is accessed up a small spiral staircase (I'm a sucker for spiral staircases...). They even have a Wii with games in an upstairs niche, which has an additional bed. They met us in person and gave us a lot of local advice and had plenty of maps and literature on the area.
The apartment is walking distance from A TON of interesting sites and restaurants, including just across a foot-bridge from the "old city". If you're up for a small hike, walk up the hill to the Roman ruins and basilica. We did it twice! There are so many awesome museums and historic buildings to visit in the area! We especially loved the Museum of Miniatures and Cinema, and the botanic gardens + zoo. There is so much to do and see that we highly recommend getting the OnlyLyon City Pass that gets you into a lot of places "for free" (after the cost of the pass itself) and gives you free access to all public transit.
The only possible downsides that you may want to consider is that the apartment is at the top of 5 flights of stairs with no elevator (not including the interior spiral staircase!!) And while the apartment is in a good location and near public transportation, it is NOT walking distance to the Lyon Part Deux train station (at least not with luggage) and Google Maps doesn't seem to have all the public transit systems so getting to the apartment initially can be confusing. Luckily, Uber is available in Lyon so it's an easy alternative if necessary.
Hopefully you won't let any of this deter you! We 100% hope to stay here again the next time we visit Lyon! We absolutely recommend you stay here too!