As per Úbeda, it was a town in Andalusia.
It still exist (in fact, it's an UNESCO World Heritage site), so it's a town.
Their excuse what they went off on a path, got lost in the hills around town and couldn't find their way back.
In order to fully understand it, I would add that the hills around Úbeda are tiny and harly anyone can get lost there.
Beat around the bush is when you are hesitant to do something (or address an issue) and you not quite sure how to go about it.
Thank you for the clear explanation.
Then this seems more appropriate for Spanish:
andarse con rodeos = beating around the bush
irse por las ramas = going off on a tangent
And
irse por los cerros de Úbeda would be on the later group too. Although, as it has already said, going off on a tangent can be a way of beating around the bush. In order words, you are hesitant about (how to do) something and you end doing something unrelated instead.
Dar largas might fit too but not necessarily. Dar largas means to delay a decision with any excuse, but you can delay it because you are hesitant about how to do it or, for example, because you forgot to make it but don't want to say it to the client...