The main difference is the usage of an indefinite article dans un bar (in a bar) while au bar includes a definite article à le bar (to the bar).

Their translation matches the indefinite article used in the English sentence, i.e. the sentence says

to a cool bar…

not

to the cool bar…

Note also that bar means either the facility (also café, bistrot, troquet…) or its counter (comptoir or a while ago zinc).

Dans can only be used with the former while au works with both.

In French there are three essential ways to use the locution "au bar". "Au bar" is the contracted form de "à le bar", which means that is read into this locution the determinative word "le".
1/ This means fundamentally, to refresh your memory in case it is needed, that the bar is a bar that the locutor has mentioned in his previous sentences. Using "le" telles to the locutors that this bar is the one he/she is talking about.
2/ Secondly, this locution implies another reference, this one most often not stated in the previous sentences of the locutor and this reference is simply the bar to which the locutor and the people he/she is talking to go usually; it is a "permanent" reference so to speak (the neighbourhood bar).
3/ Finally, as some people make it a habit to frequent bars and/or may consider it to be a habit to do so they tend to give to the word the quality of a "permanent reference" and they’ll say at times things like the following.

• Quand vous êtes au bar et que vous avez bu un verre de trop vous savez que ce n’est pas le moment de tenir tête à quelqu’un qui s’échauffe facilement. ("The bar you go to usually, I suppose you have a bar or bars, etc., any bar" In this sentence the locutor could very well have said "Quand vous êtes dans un bar …".)

• Au bar il est l’attraction principale, quand il y est, évidemment, ce qui n’est pas rare. (This makes it it clear to the person(s) listening that the locutor has a habit of going to a given bar (more likely a bar in particular and not any bar).)

In the case of your sentence ("Nous allons presque tous les samedis dans un bar sympa de notre quartier."), although the locutor makes it clear that it is a habit of his/hers to go to that bar, he/she hasn’t yet mentioned in his discourse any bar and as it is obvious too that if he were speaking to people who knew about that bar and this habit he/she wouldn’t be saying what he/she is saying, this bar is entirely un determinate for the other locutors; therefore he/she uses the indefinite article "un".