Sure, I can create a 2-day budget-friendly itinerary for Athens in November. Keep in mind that November in Athens can be a bit chilly with occasional rain, so dressing in layers and bringing a waterproof jacket is advised.

Day 1: Exploring Ancient History and Local Neighborhoods - Morning (9:00 AM - 12:00 PM): The Acropolis - Type: Historical Site - Description: Begin your day at the iconic Acropolis, the ancient citadel that overlooks the city. Visit the Parthenon, the Erechtheion, and the Temple of Athena Nike. Explore the Odeon of Herodes Atticus and the Theater of Dionysus. - Estimated Duration: 3 hours - Place: Dionysiou Areopagitou Street, Athens 105 58 - Afternoon (1:00 PM - 3:00 PM): Plaka and Anafiotika - Type: Cultural Walking Area - Description: After a quick traditional Greek lunch, wander through the Plaka neighborhood with its lovely narrow streets, and explore Anafiotika's island-like charm, known for its white-washed houses and blue doors reminiscent of the Greek islands. - Estimated Duration: 2 hours - Place: Plaka and Anafiotika, Athens 105 58 - Evening (4:00 PM - 6:00 PM): National Garden - Type: Park - Description: Relax and recover from the day's walk in the tranquil setting of the National Garden. This public park offers a peaceful escape with its shaded pathways and small ponds. - Estimated Duration: 2 hours - Place: Leoforos Amalias 1, Athens 105 57 Google Maps Link Day 1: https://www.google.com/maps/dir/The+Acropolis+Dionysiou+Areopagitou+Street,+Athens+105+58/Plaka+and+Anafiotika,+Athens+105+58/National+Garden+Leoforos+Amalias+1,+Athens+105+57/

Day 2: Beach Time, Museum, and Sunset Views - Morning (10:00 AM - 11:30 AM): Edem Beach - Type: Beach - Description: Enjoy a low-key morning at Edem Beach. While the water might be too chilly for swimming, you can take a coastal walk or simply relax by the sea. - Estimated Duration: 1.5 hours - Place: Edem Beach, Palaio Faliro 175 61 - Afternoon (12:30 PM - 2:30 PM): Museum of Cycladic Art - Type: Museum - Description: Discover the ancient Cycladic culture famous for its marble figurines. The museum has a student fee, and the first-floor collection is free on Mondays. - Estimated Duration: 2 hours - Place: Neofitou Douka 4, Athens 106 74 - Evening (4:00 PM - 6:30 PM): Mount Lycabettus - Type: Scenic Viewpoint - Description: End your day with a hike up to Mount Lycabettus for an unparalleled view of Athens. Catch the sunset, which in November is around 5:30 PM. - Estimated Duration: 2.5 hours - Place: Mount Lycabettus, Athens 114 71 Google Maps Link Day 2: https://www.google.com/maps/dir/Edem+Beach,+Palaio+Faliro+175+61/Museum+of+Cycladic+Art+Neofitou+Douka+4,+Athens+106+74/Mount+Lycabettus,+Athens+114+71/ Please verify the current opening hours and any potential entrance fees for these attractions as they can change. Also, bear in mind to check whether these sites require advance booking, especially due to seasonal variations and health guidelines.