Brussels - Ghent - Bruges - Antwerp - Rotterdam - Amsterdam

I don't think you need to change hotels so often. Several of these cities are very close to each other, Gent and Brugge in particular. Your room probably wouldn't even be ready by the time you arrived at the next hotel.

If nightlife is one of your focuses, then I would consider staying in Gent as a base for Brugge, Antwerp and maybe even Brussels. Brugge is almost dead at night, whereas Gent has a large student and young adult population to keep things hopping. My impression of Antwerp after dark is that... well, it's a rougher scene, as you might expect for a port city.

Yes, have Gent as a base. Much more lively than Brussel and Brugge. And consult www.belgianrail.be/en/Default.aspx to see that with the frequent trains and short distances make a change of hotel totally useless.
The same is true for the Netherlands, where trains run with an almost metro-like frequency. Consider staying in Leiden or Utrecht, both university cities, instead of Amsterdam, where you just a part of all those tourist crowds. See www.ns.nl/en/journeyplanner/#/ for the rail connections, including Schiphol airport.

Yes, the distances in Belgium are such that there is no point in moving between cities to stay. Pick one and make day trips to the others. Depending on how many of you there are it may be worth getting a Belgian Rail Pass, which allows you to make ten one-way journeys for 76 euros and can be shared between a group of people. (So, for example, if there are three of you making a return journey, that will use six of the ten.)

Even better, if you are under age 26 you can get a € 51 Go Pass 10 rather than the € 76 pass for ages above.

http://www.belgianrail.be/en/travel-tickets/passes-cards/go-pass-10.aspx

Like the other pass, this one can also be shared: each line must be filled out with the name/ single journey departure/destination of each traveler.

Agree!!! One or at most two bases in Belgium, one in Netherlands.