Leeds is known as a friendly city, but as with any other city, the usual tips about exercising a degree of common caution apply: leave no valuables unattended, avoid going to badly lit/shady/unknown places by yourself or walk around alone at night, etc.
There are some notorious areas of Leeds at night with seedy reputations, such as the unrejuvenated areas of Chapeltown particularly Spencer Place, a red light district, Holbeck and Mabgate. Whilst by and large these places are safe by day, it is best to avoid risking trouble.
It is also advisable to avoid displaying any memorabilia or clothing of football team Manchester United the city's football rivals, particularly in the more sulubrious parts of town though one can expect few problems around the city centre. Similarly, Leeds is an extremely proud city and disrespecting the area will almost certainly result in a hostile reaction to such comments. If you do encounter any trouble, the emergency services police, ambulance, fire number is the same as for the rest of the country: 999, or the new European wide emergency number: 112.
If you do happen to get ill in Leeds, there are of course NHS and private medical practices all across the city. The Light complex houses a NHS walk in centre and Leeds is also home to two of Europe's largest hospitals - Leeds General Infirmary in the Civic Quarter and rapidly expanding St James' a couple of miles east of the City Centre and just south of Harehills, as well as numerous smaller hospital and PCTs across the wider city area. As with the rest of the UK, tap water is safe to drink, and you are unlikely to come across any major health risks other than speeding traffic and the effects of alcohol.
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The main tourist information office for the city is in the railway station, but there are various other information points across the city e.g. Central Lending Library, The Headrow. For foreign visitors Leeds has a range of consulates, including: Danish, 6-7 Park Place, City Centre; Dutch, 12 King Street, City Centre, (http://www.mfa.nl/en/euro...); German, 1 Whatehall Road, City Centre, (http://www.konsulate.de/i...) and Greek, 8 Street Lane, Roundhay.