Take Eurostar.
It’s cheaper, and will cost you much less to get to and from on the other side then flying.
There is a train from BRU airport to the city, but it can be very slow and take over an hour.
Taxi won’t be cheap as it will be on a meter, and the traffic can be horrendous!!!
I wouldn’t fly just to try out the lounge, you will get lounge access to Eurostar, so try that one out
As to hotels, I have only ever stayed at the Hilton which has been very good, and always been upgraded to an executive room with lounge access with my HH Gold card (which I assume you got with your Platinum card?)