Talk Quesada forum

We have our NIE's and are living in Spain on a Non-Lucrative Residency Visa. Our plan is to live in Spain for several years, if possible.
We just moved into a new apartment - an unplanned move two-months after registering our first apartment's address in Spain.
Do we need to register at both the Padron office and the Police Station or only one of them? Can we do any of this online?

Both

You definitely need to change your address for the padron. This is essential.
Once you have done this, it will take about 2 months for it to go through the system (yes, things run slowly in Spain) and then you can notify all the other departments online.
Traffic department, Social Security, National Police etc can all be notified in one fell swoop.
Notifying Change of Address

Click on the link above this line and do it all in one go.
It may interest you to know that we got our NIE certificates in 2002. We have changed address twice since then and took out residency in 2011. We have never had to change our NIE certificate at all and we still have the ones with the original address on which have been accepted for padron, residency and so.