Is it safe to drink the tap water?
The golden rule is:
DO NOT DRINK THE TAP WATER!
... and that goes for ice as well.
Bottled water is extremely cheap but check that the seals are not broken before you buy. Also try not to drink directly from the bottle or can as the rim can be contaminated. The best thing to do is use a straw if possible.
You can also take iodine to add to normal tap water to purify it but some people find the taste a bit too strange. If you are planning to go on long treks it may be worth considering a water purification kit. If you are on the normal backpacking route this is not a necessity though.
Next: Staying hydrated