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For sightseeing in Amsterdam and traveling to Brussels, should we stay in Amsterdam Centraal area or can we stay at Sloterdijk station area?

How difficult and expensive it is to travel back and forth from Sloterdijk to Amsterdam Centraal?

It's quite easy to travel between Amsterdam Centraal and Amsterdam Sloterdijk. Trains are frequent and the trip is about 6 or 7 minutes. The base fare is €2.30. The travel time to Brussels is slightly less from Amsterdam Centraal because the direct trains to Brussels do not stop at Sloterdijk.

Most tourists will want to spend more of their time closer to the center of the city, though, so it's probably only a good idea to stay near Sloterdijk if your accommodation is sufficiently less expensive, or if you have something specific you want to do in the area.

I regular travel by train to Amsterdam Central, and many times, my route takes me through Sloterdijk. During the peak tourist season (roughly, beginning of April to end of October), lots of tourists take the few minute train ride between Sloterdijk and Central. Depending where in Amsterdam you want to go, you can also take tram 19. The subway also stops at Sloterdijk, but since it's the penultimate stop of the "Ringline", which circles around the center of Amsterdam, it's unlikely to be the most convenient option for sight seeing.

Trains are very frequent. During the morning rush hour, I count 22 trains/hour, dropping down to 20 trains/hour midday. It's a 6 minute train ride, costing EUR 2,30 one way (that is, if you either have bought your ticket online, or are using a chip card -- loose tickets cost 1 Euro more). Latest trains back leave Central around 1 AM.

There are a couple of large hotels near Sloterdijk; I assume they're less expensive than what's available near Amsterdam Central.

You may want to play with 9292.nl to explore your travel options.

Staying in the central area, inside the canal rings, let's you easily walk central Amsterdam and for me that works better. I love walking the central city.

The travel angle is well covered in the other answers.
From the tourist angle, I would say, it depends on what you like and want to do.

If you are the 'dinner, short travel, bed' kind of person, Sloterdijk is not bad.

But on the other hand, if you are a 'dinner, roam around, visit place to drink, visit place to listen to music, wander slowly to hotel' a central Amsterdam location will be better.

I would not even advice the Centraal Station area, but more near the Leidse plein area or around the places you will find your choice of music if not there.

Travel time to Amsterdam Centraal Station will be about the same as if staying close to Station Sloterdijk but your travel time and more importantly the ease of getting back to your hotel in the evening will make the difference.

Both areas will be safe enough, also late in the evening, but depending on the actual time of night, can feel a little deserted outside of business hours (Sloterdijk) or shopping hours, (Amsterdam centraal).

There will be public transport but the night trains do not stop at Sloterdijk, so from about 1:15 to about 5:15 you will be restricted to night buses. And those are on a one per hour schedule as far as I have found.

This is the site for all public transport in the country.

And this is the train site.