Apart from the inevitable archaeological sites, since it is not far from the Belle Epoque hotel:
In the morning:
The Athens Municipal Market:
Walking route below (5 minutes):
https://maps.app.goo.gl/WViejXVSbkzCff6S8
For lunch, in the market there are small local taverns, I suggest two:
Aris Tavern:
https://maps.app.goo.gl/nnc15rJ4bH4VWvV97
or: Oinomageireio Epirus
https://maps.app.goo.gl/DkGW4axw8cP2aLvz5
After lunch, The National Archaeological Museum (NAM), one of the largest in Europe. Ticket 12€
Walking route from Municipal Market via Athinas St and Omonia Square below (20 minutes):
https://maps.app.goo.gl/GgLpUwtHGpjR1ACp8
NAM website:
https://www.namuseum.gr/en/
If you still want to walk in Athens here is a suggestion that you won't find in the RS guide anyway:
From the NAM you are a stone's throw from the Exarcheia Neighborhood. The stronghold of the anarchist movement and Athenian counterculture.
Murals everywhere, bars and alternative shops, passing through the Technical University of Athens where the uprising against the colonels' junta began in 1973.
Don't worry, the neighborhood looks shady but is completely safe.
https://www.thisisathens.org/neighborhoods/exarchia-locals-guide
Example of a walking route:
https://maps.app.goo.gl/EZ2JoPifWxsmLGZB9
Some places to have a drink:
Kubrick Cooperative Cafe Bar:
https://maps.app.goo.gl/PgspFFFD2xBT55WF7
Raraou Cantina:
https://maps.app.goo.gl/uwiH7HBZiiGRPbFf7
Revolt street bar
https://maps.app.goo.gl/E5HnDysLSGGfo6Ee7
Return to your hotel takes around 15-20 minutes on foot.