Want to visit Baku? You're in luck. Travelling to Azerbaijan used to mean a convoluted and inconvenient visa process that turned off travellers and stifled tourism. But in January of this year the new “ASAN e-visa” system came online, allowing citizens of 81 countries, including the UK, Australia, and US, to quickly apply and receive the visa via email. Visitors who take advantage will find plenty of things to see: a cosmopolitan, affordable capital of good eats, incredible architecture – and, most importantly, friendly cats.

Here are the top 10 things to do in Baku:

The best of Baku Show all 10 1 /10 The best of Baku The best of Baku Baku's architecturally fascinating Fairmont Baku The best of Baku The cityscape Cynthia Drescher The best of Baku Zaha Hadid's Heydar Aliyev Centre Helene Binet/Heydar Aliyev Centre The best of Baku Delicious food at Sirvansah Sirvansah The best of Baku The traditional environs of Sirvansah Sirvansah The best of Baku You'll never be hungry or out of pocket in Baku Sehrli Tendir The best of Baku Friendly locals Cynthia Drescher The best of Baku The varied cityscape Fairmont Baku The best of Baku The carpet Museum Cynthia Drescher The best of Baku Getting around is easy Cynthia Drescher

Stroll the seafront

Baku sits in a natural bay on a peninsula jutting out into the Caspian Sea. The city is oriented towards the water and the breeze coming off of it, and the best stretch of waterfront is reserved for recreation and entertainment. Milli Park and its wide pedestrian promenade, named Dənizkənarı Bulvar, trace the curve of the bay and provide plenty of sunshine and space for jogging, cycling, dog-walking, and rollerblading (yes, rollerblading still a thing here). Along the route are sights like the “Baku Eye” ferris wheel, Park Bulvar mall, and the under-construction Caspian Waterfront building with its petal-like points inspired by the “sails” of the Sydney Opera House. Walk to the end to finish at National Flag Square (Dövlət Bayrağı Meydanı) with a flag and flagpole that rank among the world’s largest. Its neighbour, the massive Crystal Hall, was built for Eurovision 2012.

Eat like a king

Since 2015, Azerbaijan’s currency has halved in value against the pound. As a result, Baku is a terrifically budget-friendly city where even backpackers can afford to eat like royalty. Reserve a table within the stone arched dining room of Şirvanşah, which is as much a museum as it is a restaurant. The cocktail list may be long, but we love the fresh pomegranate juice and simple feijoa compote, the latter a sweet juice made with feijoa fruit most typically associated with Brazil. Save room to finish with a tea service and a plate of national sweets, such as the hazelnut-filled shekerbura pastry, while local musicians play traditional Azeri music. For a feast for two, you’ll find it difficult to spend even 85 manat (£40) total.

(Baku's far more beautiful than you might have realised Fairmont Baku) (Fairmont Baku)

Ride the funicular to the Flame Towers

50 qəpik (23p) is all it costs for a ride up the Baku funicular from the seaside to the three strikingly modern buildings known as the Flame Towers. One contains offices, another residences, and the third is the Fairmont Hotel Baku, though none offer an observation deck. Selfies are still compulsory up here: the funicular conveniently lets you off at Dağüstü Park, the landscaped terraces of which overlook the Bay of Baku and give the best view over the city. Time it right to catch the beginning of sunset from the foot of the Flame Towers, then take the stairs down through the park back to the seaside to the plaza next to the Azerbaijan Carpet Museum: the best spot to view the night-time light decorations of the Flame Towers (which, naturally, feature faux flames).

Drink tea

Bypass the souvenir hawkers of the Old City and descend down stone stairs to a hidden teahouse and shisha den around the corner from the Shah Palace Hotel. Low seating, Azeri wool carpets, tasselled silk curtains, and carved wood screens section off the Old Baku Tea House into semi-private nooks ideal for lounging and playing backgammon. There’s no menu, but your best bet is the “national tea set” of a pot of the house chai, delicately poured into pear-shaped glasses of cut crystal. It comes complete with fresh lemon slices, cubed sugar, a variety of nuts and dried fruits and a plate of fresh pakhlava, Azerbaijan’s version of baklava.

Have a kebab

On a nice night thousands of locals finish their day with a walk through Baku’s pedestrian zone flanked by embassies, corporate headquarters, and palatial residences in architectural styles that range from neo-Moorish to baroque. Nizami Street (Nizami Küçəsi) is nicknamed “shopping street” for all the high street shops that line it, which stay open late hoping to lure in casual browsers, but it’s also a destination for late-night snacking. Skip the “tornado potato” sticks and stop into any of the many, many döner shops for an Azeri-style kebab. Point to the paper-thin flatbread called “lavash” and pick your meat. Skewers, or “shashliks”, can be lamb, beef, chicken, fish, or veggies, but always include onions and special spices before being wrapped in the bread.

Make sure you get a real Azerbaijani carpet (Cynthia Drescher)

Haggle for a carpet

As an ancient centre of carpet weaving, you can be sure Baku has rugs to sell you. Skip the hawkers of the Old City for the shop within the Carpet Museum , where the staff can fully articulate the origin, history, and significance of the materials and design of each carpet. Prices for large rugs begin at 1000 AZN (£460), but haggling is encouraged, especially if you have your eyes on more than one. The carpet museum stocks rugs of both wool and silk with cotton, and only those handmade within Azerbaijan using traditional methods and themes. Bargaining with hawkers in the Old City may mean purchasing a cheaper rug made in Pakistan, but passed off as Azeri, and then still having to wait a day or two for the export certificate so you can take your souvenir home. The museum is able to issue the certificate on the same day.

Sightsee by subway

Public transportation may not seem like an activity you want to experience on holiday, but Baku’s tidy metro and web of underground pedestrian passages (most with escalators) make it supremely easy to pack lots of sights into one day, even if they’re across town. The underground stations themselves even showcase dramatic design, such as with the Old City’s glass pyramid and carpet-print entrance and the fluted columns of the platform at Ganjlik Mall, the largest mall in Azerbaijan. Best of all, transport is cheap – a four-ride “BakıKart” costs 1 manat (£0.46).

See Zaha Hadid’s architecture

This is the setting for your next Facebook profile photo. The Heydar Aliyev Centre (Heydər Əliyev Mərkəzi) is Azerbaijan taking a hard stance against the brutalist Soviet architecture of its past for a future of beauty and technology. It’s a masterwork of Zaha Hadid’s firm and stunning from every angle, inside and out. And you must go inside. Entry is 15 manat (£6.90) and for the fee you’ll be able to access an exhibition on Heydar Aliyev, a floor of detailed scale models of Azerbaijan’s most important architectural works, and a small museum showcasing Azerbaijani crafts, customs, and culture. Finish your visit by prancing through its gardens of modern art sculptures, flower fields, and waterfalls while taking another few hundred photos of the building.

Instagram your way around the Heydar Aliyev Centre (Helene Binet/Zaha Hadid Architects)

Eat Azeri cuisine

At Sehrli Təndir restaurant in the Old City, the menu is a list of everything you shouldn’t leave Azerbaijan without tasting. Definitely do the dolma (aubergine, linden leaves, grape leaves, or peppers stuffed with meat, onion, rice, herbs, and mint, then topped with a dollop of cool yogurt), plov (buttery rice pilaf with meat, chestnut, and cooked fruit), and the ubiquitous kebabs. The star of the show here, however, is the open tandoor oven at the entrance, where the restaurant’s resident baker tends to the breads cooking inside.

Cat-spot in the Old City