A European city break for £100 is a berserk prospect. Berserk. That's a return flight and a two-night hotel stay for less than the cost of a train to Scotland. The thought of exactly what that would get you – a damp floor in a windowless room in a no-star brothel, with a rat the size of a toddler – is almost enough to put you off completely.

And yet easyJet seems to have pulled it off. Until mid-September, it's running a scheme (holidays.easyjet.com) that offers two-night stays in destinations like Berlin, Seville and Prague for £100pp. I ventured to Tallinn for my weekend away, vowing to spend as little cash as possible. But would this financial constraint mean that it'd all be a bit, you know, crap?

Getting to Stansted for a 7am flight (and an easyJet flight, too, with its traditional elbows-out, free-for-all boarding policy) is never fun, but at least Tallinn is just three hours away. My hotel, though, was deeply impressive; the towering, four-star Radisson Blu Olümpia (radissonblu.com) in Tallinn's business district. It's a 15-minute walk to the sights, but it's bright and clean and full of photos of former visitors, like Hillary Clinton and Richard Clayderman. As bargains go, it's ridiculous. The real test was seeing how well Tallinn lends itself to someone as impossibly tightwaddish as me.

Free stuff

Although small, Tallinn is a beautiful, knotty, walled medieval city that's rich in history. To orient myself, I turned up for the Tallinn Free Tour (freetour.traveller.ee), which starts from Niguliste each midday. Run by student volunteers, it's a lively and irreverent two-hour trot around all the main points of interest, punctuated by a kaleidoscope of off-kilter local insight. My guide, Anne, was a whirlwind of facts and stories and politically incorrect observations, including one about an Estonian national hero whom she gleefully referred to as an idiot with a drinking problem.

Tallinn is also the 2011 European Capital of Culture and last weekend marked both the 20th anniversary of Estonia's independence from the Soviet Union and Iceland's recognition of Estonia as an independent state (the first country to do so), so there was a glut of free stuff to crash. On Sunday, for example, I caught an acoustic set by Icelandic folk singer Snorri Helgason in the gloriously sun-dappled Masters' Courtyard, while screenings and food markets and parties went on elsewhere.

Estonia is good at this – its tourism website is full of similar events – and for the miserly traveller, this sort of thing is the mother lode. But if that's too much like hard work, Tallinn is stuffed with free wi-fi hotspots, so you can always just sit in a park and gnaw on pilfered breakfast rolls while you watch cat videos on YouTube all day.

Food

Estonia might have a long and rich gastronomic heritage, but when you're as stingy as me, that doesn't mean a lot. Fortunately, the package covered the Radisson's bountiful Super Breakfast Buffet, so anyone truly operating on a shoestring could quite easily load up on eggs and meat and pancakes and porridge and spend the rest of the day plodding it all off.

For the sake of variety, I did venture out for actual paid-for food. Vapiano (vapiano.de/frame.php?lang=ee) is a constantly thronging chain of ridiculously cheap Italian restaurants serving giant, delicious pizzas from €4.50. There's also the Krug Inn, tucked away inside the town hall. Lit by candlelight and impossibly small, it sells just two dishes – elk soup and pies. Both are delicious and cost just €1, but the kitchen is so small that pie batches sell out almost instantly.

Kompressor on Rataskaevu is a pancake house that everyone recommends. It's not hard to see why – the pancakes are planet-sized. A ham and cheese pancake will make you uncomfortably full for just €3.80. However, being both stupid and greedy, I also ordered a plate of superfluous deep-fried cheese balls for €2.40 that, while delicious, may as well have been rammed directly into my aorta. TripAdvisor favourite Von Krahl Aed (vonkrahl.ee/) is a cosy little courtyard restaurant on Rataskaevu that does a chicken and egg sandwich for €3 and a frozen cheesecake for €3.50. Then, coming home, Tallinn airport offers the choice of a cheeseburger with cabbage, or a French hot dog. You'll eat the cheeseburger because it looks less like an erect dog penis. It's €4.20, and not as awful as it sounds.

Drink

Tallinn has a stag-party reputation completely at odds with how pretty and quaint it is. So I ventured into town on Saturday night and braced myself for awfulness. First came Shooters (shooters.ee/), a sticky-floored studenty dive vibrating to the sound of Beyoncé, and specialising in trays of five shots for €5. I chose a sour apple vodka thing, and knocked them back as fast as I could to escape the British bloke in a nightie who kept shouting about all the foreign girls he was planning to nail that night.

Much better was Hell Hunt (hellhunt.ee/), which translates as Gentle Wolf, on Pikk Street. It's apparently the oldest pub in Tallinn, and definitely one of the busiest and cheapest. Get there early enough and you can nab a sofa. Smile enough and the waitress will start inventing cocktails for you.

Miscellaneous

This summer, above the Viru Keskus shopping centre, there's an open-air rooftop film festival (katusekino.ee/), where locals gather to sit on deckchairs, drink beer, wrap themselves in blankets and watch movies that aren't widely known in Estonia. A week earlier and I could have seen Rosemary's Baby. A week later and it would have been Breakfast at Tiffany's. But last Friday it was Hunnik, Pappi ja Suitsev Kaheraudne - or Lock, Stock and Two Smoking Barrels. Yes, look, there was a Guy Ritchie season. I never said it was perfect.

Elsewhere, travelling even slightly north from the city walls brings you into a different world. The Kalamaja district is home to a daily flea market, purportedly full of hipsters but actually just rammed with horrible clothes, old typewriters, bicycle handlebars, Soviet-era porn and hundreds of downbeat pensioners. It's also by the sea, where there was an indecipherable youth theatre production on a yacht, a pop-up cafe in a bus, and some people spray-painting a shipping container. It's not essential, but it's diverting.

For souvenirs, you basically have the choice of traditional hats and scarves, or bits of tat shaped like either a viking or a Russian doll. I ended up buying a little wonky-eyed velvet elk with metal teeth from Nukupood (nukupood.ee/), a doll shop next to the town hall. At €10, it was the most expensive single purchase of my weekend, but hopefully it'll haunt the nightmares of my unborn offspring for generations to come.

Total spent, including flights, accommodation, food, drink and souvenirs: £167.43.