During our winter week in Athens, the wandering around was for us about food, views, and cats. All of which were plentiful, pleasant, and welcoming.
We typically traveled around the Plaka, Syntagma, and Monastiraki, which are really the primary tourist/historical districts.
Since we were visiting as a family, typically our restaurant meal was midday, and we’d cook at the apartment for dinner. So no fancy dining recommendations below; just cafes, ice cream parlors, and take away souvlaki.
The Plaka
Plaka, the oldest neighborhood of Athens, is also a restaurant favorite. If for no other reason than outdoor seating ambience, dining in Plaka is very worthwhile.
Restaurants
Some places we recommend, Yiasemi, Dickie Dee’s, El Greche, and Kostas.
My favorite spot in Plaka was Yiasemi, for their orange pie. We went twice during our visit so I could order it again. And very possibly we also bought some at a bakery and took it home with us. I might be obessessed.
Around Syntagma, we ate at the mega-famous Kostas souvlaki joint, which more than lived up to its reputation.
And my girls absolutely adored Dickie Dee’s ice cream, where they ordered a soft serve cone with a halo of cotton candy surrounding it. What could be better?
Right around the corner from Dickie Dee’s was a truly fantastic gelato shop, La Greche, where I got my preferred flavors a couple times.
Street Art
We saw lots of great (and some less great) street art throughout Athens. Here are some of my favs.
Syntagma Square
Watched over by the Hellenic Parliament building, Syntagma Square is where one can view the elaborate changing of the guard ceremony on Sunday mornings.
The parliament building was originally the royal palace of King Otto, the first king of Greece and, consequently where the Athenians rose up against King Otto of Greece on 3 September 1843 to demand a constitution.
Mount Lycabettus
Further out from the main historical districts in Athens one finds the Lycabettus Funicular. Up Mount Lycabettus you climb, the funicular taking passengers up to the highest peak in central Athens. On the top of the mountain you’ll find the Chapel of Saint George, a tiny chapel first used in 1834, which sits atop the grounds of an ancient temple of Zeus. We took the funicular up, and then hiked down; a great way to explore the area with kids. 
Shopping
We aren’t big shoppers, but there are a few places I recommend in Athens. Everyone talks about the Monastiraki flea market area, and we did walk around there, but I find it rather overwhelming. I mush preferred the street vendors along the street circling the Acropolis, and a few other small spots. One is Amorgos Antique Store, which is filled to the brim with authentic Karagiozis shadow puppets. They are beautiful, and yet always a bit too expensive for me, but the shop is worth a stop, and the woman inside was so kind, explaining which characters were which to my daughters.
One other shop I recommend is, surprisingly, the gift shop inside the Acropolis Museum. Not only do I like shopping in a place that will support the museum, but the prices were unusually good. They carried an assortment of Playmobil Greek gods and goddesses, which my kids thought were just too cool, at €4 apiece. On Amazon.de they list at about €13/each, so needless to say we purchased more than a few as a surprise.
Lastly, we stopped in to purchase some handmade sandals at Stavros Melissinos, the Poet Sandalmaker of Athens. Practically a historic institution at this point, Rudy and I had bought sandals at the original shop over 10 years ago, and we were eager to return. The little one decided on a pair, too.
The neighborhoods of Athens have so much to see and enjoy; you can get lost wandering in circles through the small streets of Plaka, or stopping for wine and snacks in Monastiraki. 
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