I stole this explanation from StartSpanish.com. There have been questions when to use sino opposed to pero.
Sino (but) Sino connects two opposite or contrasting ideas (like pero) but only when the first clause is a negative statement and the second is affirmative.
No bebo café sino té. I don’t drink coffee but tea. Hoy no quiero ir al cine sino a caminar. Today I don’t want to go to the cinema but (I want)to walk.
I think I was taught to think of "sino" as "but instead" and that generally works (I don't drink coffee, but instead tea).
Sino is an elegant way to provide a non-obvious alternative to a negative statement, without having to start a new sentence.
To avoid confusing it with pero, try replacing it with although–if it works, it's pero; otherwise, it's sino.
> — Me apetecía verte hoy, pero hasta mañana no puedo.
> "I felt like seeing you today, (but/although) until tomorrow, I can't."
> — Pues yo no contaba con verte hoy, sino mañana, así que perfecto.
> "(Well) I wasn't counting on seeing you today, (but/I was counting on seeing you) tomorrow, so that's perfect."
I go deep into the usage context of sino in this NachoTime post.