You have a variety of options in front of you if you would like to go from one place to another in the center of Athens
You could use Metro,Tram, Bus, Electric Railway&Trolley
Firstly, there is the Metro&Electric Railway which is the fastest way to get yourself quickly between main points in the city center but its a little bit crowded. In your first use it can be a little bit troublesome to navigate but as you are getting to know it you will find it pretty simple.
The Tram is the safest way to get yourself to the beach areas along the coast from Syntagma square, also it’s a very good way to get to know Athens and the Coast’s(Tram is connecting the Syntagma Square with Voula-South coast of Athens&Piraeus-The Port)
Thirdly there is the Bus&Trolley option that can get you pretty much everywhere both allow cross ticketing from any of the public transport networks so if you have a metro ticket, you can use it on the buses. You may find them confusing in your first use so i suggest you try downloading an app on routes/maps/time scales so you won’t have trouble of finding your way out(Useful Applications in Athens)
If you don’t want to use public transportation there is always the taxi option(yellow in colour), i suggest you downloading either Taxibeat available on Android/Apple Store or Uber in order to avoid any misunderstandings with the greek taxi-drivers