I was in the middle of the Helsinki's Design Forum shop – eyeing up a teapot of such an ingenious merger of ceramic and wood that it almost seemed to justify the €100 price tag – when I was startled by the roar of a chainsaw behind me. The hubbub turned out to be chair-maker Jouko Kärkkäinen doing an impromptu demo, fashioning a stool from a block of wood with a few deft slices, before sitting down on his new creation to a round of applause.

It looked effortless and fun – and exactly what you'd expect to see at a foundation that brings together contemporary Finnish artists and designers, in a city so infused by design it was recently awarded World Design Capital status for 2012. There's good design everywhere in Helsinki, from quirky high chairs for cultured nippers in the cafe at the Kiasma modern art gallery to Eliel Saarinen's magical central train station, which is guarded by lamp-bearing giants carved from granite that inspired Gotham City in the first Batman film.

Helsinki deserves its sobriquet "Pearl of the Baltic". The shoreline curls through a succession of harbours where massive ice-breakers tower over sleek yachts and historic sailing ships. Ferries whisk you out to pleasure islands such as Pihlajasaari or the Unesco world heritage fortress of Suomenlinna, the 19th-century garrison which now houses craft shops and museums.

Back from the sea, Helsinki mixes and matches ravishing architectural styles, displayed on wide streets lit by the distinctive northern light. The ornate facades of Jugendstil (art nouveau) are everywhere, especially the pastel-hued houses in the Eira neighbourhood.

Clean-lined Scandinavian modernism is most famously showcased by two buildings. The Finlandia Hall, created by wavy vase designer Alvar Aalto between 1967 and 1972, perches on one side of Töölönlahti, the city's central lake, across from a clutch of graceful 19th-century wooden villas. By the northern end of the lake, the functionalist Olympic stadium merits its own gold medal.

And then there's the traditional Russian ambience of a city that filmmakers used as a stand-in for St Petersburg in films such as Doctor Zhivago and Reds. In the vast Senate Square, a block from the bustle of the harbourside Market Square, you see why as you crane to take in the grandeur of the snow-white Tuomio church and the contrasting onion domes of the nearby Uspenski cathedral.

But I wasn't just here to enjoy one of northern Europe's most beautiful capitals; I was on a mission. As a cash-strapped connoisseur of Scandinavian style with just €100 in my pocket, how much vintage Finnish design, from sinewy glass to dazzling textiles, could I tick off my wish list?

Hunting places are ten-a-penny. If only the prices were that cheap. The epicentre of Helsinki style is Punavuori, a neighbourhood now officially branded as the Design District, with more than 150 bars, cafes and hotels in a compact grid of streets stretching from Mannerheimintie, the city's central boulevard, to the harbourside antiques hall and flea market at Hietalahti.

The new stuff at shops such as Aero (Yrjonkatu 8) was eye-catching but expensive, although €6 bought me a fab poster of Aalto chairs in lieu of the real thing. A quintessentially Finnish lunch followed – delicious herring at the beautifully retro Ravintola Sea Horse (Kapteeninkatu 11, ).

Within 10 minutes of entering the higgledy-piggledy Helsinki Secondhand warehouse on Korkeavuorenkatu, I was clutching my first finds – a dinky Arabia milk jug for €8 that's pretty enough to display on its own, plus a gorgeous 1960s geometric vase by noted designer Pentti Sarpaneva for €20. And if I'd had a crate and a ship handy, I'd have cleaned the place out of all the exquisite furniture.

At Haddadin on Iso-Roobertinkatu I understood the "Do Not Touch" signs on some shelves when I realised the collectable Iittala glass I was salivating over cost thousands. But just as I was about to leave empty-handed, I spotted a 1970s Kumela "Rock" vase, and was astonished to be told it cost just €10, thanks to a tiny chip I hadn't noticed. Nor did I care and into my bag it went.

I bagged more vintage glass – a quirky bowl by the innovative Muurla factory – for the same price at nearby Viva Design (Albertinkatu 12). A gorgeously streamlined Pentik pot (€30) prompted an agony of indecision, but weight worries won out over design lust – a rare triumph of common sense that I am still regretting.

I rounded off the afternoon at the Design Museum, carved out of an unassuming old building back on Korkeavuorenkatu. I could only dream of owning the stuff in here, but I saw how Finland's design nous grew out of 19th-century farmhouse crafts – functional objects made simply but with style.

The following morning, I switched from the past to the future at the autumn Habitare design exhibition (1-5 September 2010), showcasing intricate laser-cut wood, dazzling lights and ravishing new textiles. Afterwards, I mulled it all over at the equally innovative restaurant Juuri (Korkeavuorenkatu 27), which has created Finnish tapas (sapas) such as raspberry marinated arctic char with radish sauce for under €5 apiece.

There was also an antique shop next door, where a rummage unearthed the textile part of my wish list – several square metres of psychedelic "violetta" fabric from Sellgren for €25. It's more leftfield than anything by Marimekko.

Helsinki's famous Hietalahti flea market, in front of the square's indoor antiques hall, is stuffed with covetable classics. Alas, budget ruled out the 1920s Arabia plate for €55 on one stall, though it's a fair price given that an hour later I was gazing at another one on display at the Arabia factory museum and gallery (Hämeentie 135) showcasing 130 years of the company's creations.

A 20-minute tram ride (the No 6) out to one of Helsinki's green suburbs, the museum is part of a complex that includes discount outlets for Iittalla and Pentik (up to 25% off city centre prices). It's also home to Helsinki's school of art and design, and the museum curator seemed surprised that I would even ask whether the students and companies work together, as she showed me the superbly equipped studios attached to the gallery space.

Back in town, I caught up with Finland's newest arena for dazzling design-couture. At Miun (Uudenmaankatu 14), designer Ilona Hyötyläinen told me how she came up with the shop name ("Mine") after crying the word out in delight when she first saw someone wearing one of her early creations. Directly opposite, Ivana Helsinki is a striking technicolour-tiled space for the first Finnish brand to hit the Paris catwalks.

With an hour until I had to head for the airport, I grabbed coffee and cake at the Kiasma gallery. The sunlight emphasises the cafe's simple beauty – transparent green chairs luminescent against a brightly painted ochre wall, artful jugs and vessels arranged along a shiny zinc bar. Even the locals looked like the work of someone with vision – high sculpted cheekbones, eyes with colours unknown to Farrow & Ball. You just can't escape good looks in Helsinki.

• Finnair (0870 241 4411) and British Airways (0844 493 0 787) fly to Helsinki from Heathrow and Manchester. EasyJet flies from Manchester and Gatwick. The Hotel Torni (+358 201 234604) has double rooms from around €89.50pp pn B&B. Further information: visitfinland.com, visithelsinki.fi and Design District Helsinki.

• This article was amended on 25 June 2012 to remove an incorrect correction which had been added to the top of the article. The correction misunderstood the term "Scandinavian modernism".