I used to think of Athens as a big ugly city with obligatory ancient sights, fine museums, the Plaka (the extremely touristy old center) and not much else. “The joy of Greece is outside of Athens,” I wrote. “See Athens’ museums and scram.”

But with each return visit I enjoy the city more than ever before, having realized that it’s a many-faceted city that’s getting its act together, still building on the infrastructure improvements it’s enjoyed since hosting the 2004 Olympics.

I discovered much of that energy in the offbeat neighborhoods just outside the tourist-packed core, largely thanks to the summer visit when I met Matt Barrett, who splits his time between Greece and North Carolina. He splashes through his adopted hometown like a kid in a wading pool, enthusiastically sharing his discoveries and observations on his generous website, Athens Survival Guide.

He took me to Exarchia, a student district just a short walk from Omonia Square, on the north end of the city’s center. This area has long been the locus of Athens’ nonconformist past and fertile ground for keeping its feisty free-spiritedness alive. Slathered in colorful graffiti, it’s defiant, artsy and full of life.

From the small Exarchia Square, side streets spin off into grungy neighborhoods. Because of the cheap rent and abundance of students (three universities are nearby), the streets are lined with cafes, bars, art centers and bookstores. Each evening, Exarchia is a thriving festival of alternative lifestyles. The juxtaposition between Exarchia and the adjacent upscale diplomatic district of Kolonaki is striking.

The Psyrri district, closer to the Acropolis, is a swankier neighborhood. Until recently, it was a grimy area of workshops and cottage industries, famous locally as a hotbed of poets, musicians, revolutionaries and troublemakers. But now it’s become one of central Athens’ top after-hours zones. The mix of trendy and crusty gives the area a unique charm. The options include slick, touristy tavernas with live traditional music, highly conceptual cafe/bars catering to cool young Athenians, and clubs with DJs or live music for partying the night away.

Just beyond Psyrri, Athens’ Central Market isn’t cute or idyllic, like a small-town French halles, and it’s not nearly as touristy as, say, Barcelona’s La Boqueria market. The Central Market — an 1886 glass and iron arcade with surrounding lanes — is refreshingly real: a thriving marketplace where workaday Athenians stock up on ingredients. A walk through the market is a treat for all the senses.

The spice sellers are the great-great-grandchildren of those ethnic-Greek refugees from the Greco-Turkish war of the 1920s, who arrived bringing a pungent whiff of exotic Istanbul bazaars.

You’ll see bushels of rice, grains, nuts and dried fruits. Keep an eye out for bunches of partially dried flowering herbs tied up with string — this is Greek mountain tea, an herbal mixture revered for its healing properties. You’ll also see classic Greek oregano, thyme, basil and the precious Greek red saffron.

The meat and fish hall, the gut of the market, is a vivid parade of proteins. Vegetarians might want to skip this section. Tables are piled high with beef, pork, chicken, lamb and goat, and livestock is proudly pictured on some signs above the stalls. Little delivery scooters nudge their way past pedestrians.

Around the corner, displays do their best to make the “fifth quarter,” or hard-to-sell meat, look appetizing: hooves, tripe, liver and other organs. You may also see barrels of snails — a cheap source of protein during times of hardship, when locals developed a taste for the little critters that persists today.

Close by, the pleasant, pedestrian-friendly Aiolou Street, quieter than the parallel Athinas drag one block over, is emerging as one of downtown Athens’ most appealing streets. It bustles with interesting stores, designer coffee shops, occasional street musicians and lots of lunch-focused restaurants for busy urbanites. You can take a break from the heat in the petite, gorgeously restored Kimisi Theotokou Chrisospileotissis church, with a beautifully serene interior. Back outside, the little square of St. Irene — the epicenter of hip, young locals, day or night — used to be known as the square of the flower vendors; these days only one remains open, and it’s still loyally frequented by Athenians.

Today’s Athens has become a people-friendly urban scene of pedestrian boulevards and squares filled with benches, shade-giving trees and inviting cafes. While its drawing power will always be its classic ancient sights, in-the-know visitors make time to also taste the spicy neighborhoods where modern-­day Athenians thrive.

Rick Steves writes European guidebooks and hosts travel shows on public TV and radio. Contact him at rick@ricksteves.com. His column runs on alternating weeks in the Travel section.