Helsinki is a fascinating combination of influences that aren’t found elsewhere and it’s clean and well organized, but it’s notoriously expensive as well. From a visitor’s perspective it’s not quite as expensive as Stockholm, but compared to nearly anywhere else in Europe it will seem pricey.
Hotels in Helsinki are quite expensive by most standards, but at least the quality is usually very high so you may not feel like you are being taken advantage of. It’s tough to find a real budget hotel, though if you are coming on a weekend you might find prices at the nicer places are within your range since so many business travelers aren’t in town. Hostels are all fairly expensive by international standards as well.
The main attractions are actually quite inexpensive, with many of the better museums in the city actually being free similar to those in the United Kingdom. Food and drinks will, unfortunately, eat into your budget, so those on a backpacker fund will want to seek out casual places rather than the sit-down restaurants in the tourist area.