Hola AA

The use of unos and algunos, although sometimes are perfectly interchangeable if you don't go into the very small connotations, differs, but to see where it would sound better to use one or another there are quite a few elements to bear in mind. 

Here is an excellent article by Español Avanzado, where they explain all these very small nuances. You will see from the beginning that there are lots of different things and scenarios to consider. 

I have taken out one of their sentences from the article that clicks nicely with what you found in our writing challenge. As you can see, in this case, the nuance is minimal. As we don't have so much space to indicate which specific nuance we want, we admit both "unos" and "algunos" in that phrase in the translation. 

This is the similar sentence:

-Este verano vamos a pasar unos días en la playa [Un grupo de días]

→Este verano vamos a pasar algunos días en la playa [Quizá días sueltos]

The second one, using algunos "may" have the connotation of spending some days that may not be correlative, but one day, then another day a bit after, etc. 

With reference to "varios", I would say it is more directly translated as the English "several". So, the difference between using "varios" and "algunos" is the same as in English when using either "several" or "some":

I spent several days at the hotel. vs I spent some days at the hotel.

There are also other synonyms:

unos pocos días, unos cuantos días,... that generally translate as "a few", but also as a more general "some".

 

I hope this helps.

Saludos cordiales