Costs
The current exchange rate of the British Pound (GBP) will make perhaps the biggest difference to foreign visitors, but even then York is, by English and global standards, fairly expensive for visitors.
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At the budget end (staying in hostels, rarely eating out, walking and visiting mostly free sights), you might be able to get away with about £60/person/day in high season.
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A more average budget for most visitors (staying at standard hotels or B&Bs, eating out once a day, going to the full range of sights and taking public transport), would be around £150/person/day.
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At the upper end, double that again. With £300/person/day you'll get a pretty high-end experience, with smart hotels, meals at the full range of restaurants, sights and taking taxis around town whenever you feel like it.