I'm often in Athens, and I rarely take the metro to get around town. I usually take the bus; there are 50 times more bus stops than metro stations.
Although the most pleasant way to see the city is on foot, you can indeed take the metro from Omonia Square. But if you want to enjoy the city in a more pleasant way than going underground, it's much simpler to take the bus. Plus, you won't have to worry about pickpockets, who only operate on the metro. And there are no stairs to get on the bus.
Don't worry about not knowing where to get off the bus; the buses have electronic displays that show the bus's real-time location and the next stop in English and Greek. The next stop is also announced in English over the bus's loudspeaker.
Here's what it looks like when bus 35 arrives at Omonia:
https://photos.app.goo.gl/RbW6j19Eg6Pjv4id8
Then at Monastiraki a few minutes later:
https://photos.app.goo.gl/k3iWroZfAJC1noi29
It couldn't be easier. Like everywhere , you just press one of the designated buttons to request the stop at the next bus stop. You won't be the only ones wanting to get off anyway.
Next to the Melia Hotel, on Patision Avenue, there's the Polytechneio bus stop for line 35, which takes you to Monastiraki Square. The bus stop is here, in front of the Rodolfo Valentino store.
https://maps.app.goo.gl/qy6TDsrYmDk9TwPs6
You can take it in the opposite direction to return to the hotel. In this direction the bus stop is located on Septemvriou Street.
The route for bus 35:
https://citymapper.com/athens/bus/bus-035
From Omonia Square, you'll have even more bus and trolleybus options. For example, trolley lines 1 and 12 go to Syntagma Square.
Use the Citymapper app, which is very reliable for planning a route (more so than Google Maps' bus directions).
https://citymapper.com/athens
Since last year, paper tickets are no longer required on any public transport. You can use your contactless credit card (Visa or Mastercard only), your smartphone with the Apple Pay or Google Pay app, or your Apple Watch.
https://www.oasa.gr/en/tickets/products/contactless-payments-with-bank-cards/
Validate your journey as you would with a paper ticket.
Each metro or bus journey costs €1.20 and is valid for 90 minutes. with a maximum daily charge equal to the cost of a 24-hour ticket (€4.10), regardless of the number of public transport trips.