quedar vs quedarse
Quedar is what's left or how something fits. Quedarse is staying put. One letter pair, two different ideas.
quedar
To be left over, to remain, to fit or look on someone, or to be located.
Quedan dos días para las vacaciones.
There are two days left until the holidays.
What remains. Works like gustar: the days are the subject, so it agrees (quedan).
Esa chaqueta te queda genial.
That jacket looks great on you.
Quedar bien/mal = to fit or suit. Different from sentar, which is more about comfort and agreement.
¿Dónde queda la estación?
Where is the station?
Quedar for location is very common in Latin America and increasingly in Spain.
quedarse
To stay, to remain in a place or state, or to end up somewhere.
Me quedo en casa esta noche.
I'm staying home tonight.
You choose to stay. The reflexive marks the subject staying put.
Se quedó sin batería.
It ran out of battery.
Quedarse sin = to run out of / end up without.
Quédate con el cambio.
Keep the change.
Quedarse con = to keep or to take (an option). '¿Con cuál te quedas?' = which one are you going with?
Tricky bit
'Me quedan cinco euros' (I have five euros left) vs 'me quedo con cinco euros' (I'll keep five euros). The first is what's left; the second is your choice.