Hmm.... I guess it depends on why you reckon it doesn't taste nice! It won't be because it's hard water, nothing wrong with that. In fact, different beer styles have evolved to use different water types (examples are Burton beers - lots of dissolved salts in the water - versus say Guinness, where the style suits a softer water). But don't get hung up on this just yet!
Is the nasty taste because it tastes strongly of chlorine I wonder?
Anyway, if you think the filtered water from your fridge tastes fine, then I'd say that your best bet is to use that, at least to start yourself off. Don't worry about hardness, you'll get a decent brew. Plus, if the water tastes nice to you, it'll boost your confidence that the beer will also taste nice!