Although the Slovak government does not require visitors to have any mandatory vaccinations (other than yellow fever, and that too if you're arriving from an infected zone), you might be wise to check with your doctor before you leave for your trip. There are two main health risks in Slovakia, Lyme disease and encephalitis, and if you’re likely to be at risk, it’s best to get immunisation done. The water in Slovakia is quite safe to drink- the tap water in Bratislava is reputedly safer than that in New York City, but steer clear of anything, like mayonnaise, which may have raw eggs- salmonellosis is not uncommon. If you’re going trekking or on other outdoor activities, watch out for ticks- they can cause encephalitis; should you get one, don’t try pulling it out- get to a doctor as quick as you can.
The medical system in the country is competent enough, but you might face some difficulty finding a clinic or a pharmacy where English is understood- so be prepared. It’s also a good idea to get medical insurance done before you set off on your trip- it can make things easier if you should fall ill.
Although violent crime towards foreign tourists isn’t much of a problem in Slovakia, petty theft is. Always keep your hotel door (and your suitcase) locked, and keep an eye on your valuables. Don’t show off your wealth, and if you’re moving through a crowded area, keep a firm grip on your wallet. Other than that, it’s wise to make a note of the telephone numbers of the local police station and your embassy. In the past few years, due to the rising social discontent, unemployment and economic disruption, a lot of locals have started viewing foreigners as easy prey for theft, so you should be doubly careful.