Cuba is a country a lot of people know at least a little about. The thought of it might conjure up images of Castro, Che and revolution, of rum and dancing, of beaten-up retro American cars, or maybe fine (possibly even exploding) cigars. But it's unlikely many people would be able to name even one national dish.

I visited a few years ago and struggle to call to mind anything other than mores y cristianos, a side dish of black beans and rice. To be honest, bar a couple of pleasant exceptions in people's homes, food in Cuba was generally pretty bad.

With this in mind then, how is it that Viva Cuba – a Cuban restaurant on the not particularly glamorous Kirkstall Road – has managed to do so well?

Sitting down at a table early on a Saturday evening, the answer is immediately obvious. There are two reasons for its success. Firstly, the menu reveals it's not exactly a Cuban restaurant – it's actually Cuban and Spanish fare on offer. Tapas, in fact. And, although there are some concessions to the Caribbean, it's the Spanish side wearing the trousers. This explains a lot – people love tapas because it's social, informal, easy and, for many, familiar.

The second reason is that, while the food feels Spanish rather than Cuban, everything else – the drinks, the music, the atmosphere – feels very Cuban indeed. Which, as far as I'm concerned, is very much the right way round. The fact that the restaurant is regularly full by about quarter past six suggests many other people agree.

We pick a table in a corner and survey the scene: a bustling restaurant on a sultry early summer day, ramshackle but comfy furniture, lots of dark wood, colourful iconography wherever you look and brilliantly evocative Cuban folk tunes playing away in the background. With the back door open to let a breeze through, the place is quite simply like being on holiday, and I find myself unable to do anything other than order a mojito, that rum, mint, sugar and soda cocktail which seems to have taken the world by storm. Rightly so, for it is a great drink and the folk at Viva Cuba happen to make them perfectly.

Once we've soaked in enough of the atmosphere to have truly forgotten the outside world, we try our best not to order everything on the menu. Heeding the advice of our lovely waitress, Kim, we order about half a dozen dishes, starting with a bowl of fat and deeply savoury olives to pick at while we wait. The wait isn't long however and soon our table is covered in bowls and plates.

Patatas bravas are exactly as they should be: cubes of chip-like potato smothered in a spicy tomato sauce. They don't hold any surprises, but then they rarely do and, well, it wouldn't be tapas without PBs. Another usual suspect, albondigas (or meatballs), is a second guilty pleasure type option – finesse free, but good, solid, dependable comfort food that doesn't disappoint. The only puzzling thing is that they're described as Cuban meatballs, yet they seem no different to what you'd get in any neighbourhood tapas restaurant.

Gambas y plancha, griddled prawns, make this a hat-trick of predictable, text-book tapas ordering that we should probably be slightly ashamed of. Perhaps it's this feeling that we're on holiday. Clichéd dishes they may be, but they are all competently put-together. The prawns stand out in particular for their size and juiciness.

In a bid to at least try to make the food element of this experience feel slightly Cuban, we order salt cod fishcakes in a lime and coriander salsa. One bite in and we're very glad we did so – they're chunky, wholesome and more-ish, with the fragrant salsa lifting the whole dish. A Cuban bean stew sounds massively unexciting, but we order it anyway in the same spirit. It turns out to be the star turn: plump chunks of aubergine and a plentiful supply of satisfying beans swimming in a spicy tomato stew that bursts with flavour. Those patatas ought to feel humbled.

Of all the dishes only one strikes a truly duff note: grilled red peppers stuffed with herby feta, an option from the specials blackboard. We can't work out whether it's the peppers, the cheese or both, but they're saltier than the table salt and we steer clear. We're not too bothered – that's tapas, after all. You order a bundle of things and if one's not to your liking, it doesn't have to scupper the whole meal.

Desserts have a feeling of afterthought to them, though they're not bad. A chocolate bouchon is a dark choc sponge with an oozy choc centre that's sweet but surprisingly not that chocolaty, and an iced tiramisu is a nice light finish to the meal, but doesn't taste of coffee very much. At £3.25 they're cheap enough for this to not feel like an outrage, but next time I go, I won't bother with dessert.

On the subject of low prices, at under £50 for a feast including a mojito, a Cuban beer and a couple of soft drinks, it's clear that the average bill is a third reason why this place continues to fill up night after night, year on year. The food's a little rough around the edges, true, but the atmosphere is something else. I'd become a regular just for those mojitos.

Viva Cuba, 342 Kirkstall Road, Leeds, LS4 2DS, 0113 275 0888.