Learn Turkish: Bu barda müzik çok güzel. - The music in this bar is very nice.

In Turkish, the present tense "to be" for the third person ("is") is often just implied. You don't need a verb at the end of the sentence. You could technically add the suffix -dir and say güzeldir, but in everyday spoken Turkish, leaving it as just güzel is completely normal and actually more common.

Doesn't güzel mean "beautiful"? Why is it translated as "nice" here?

While güzel does mean "beautiful" when talking about people or places, it is used much more broadly in Turkish to mean "nice," "good," or "pleasant." Just like in English, you can have a güzel meal, a güzel day, or in this case, güzel music.

Since barda has the locative suffix -da (meaning "in"), shouldn't bu ("this") also take a suffix?

No, Turkish adjectives and demonstrative words like bu never change to match the noun they describe. The case ending only goes on the noun itself, so it is always bu barda (in this bar), never buda barda.