I live near Conrad. On arrival at BKK, I always take train to Makkasan. It is then an easy walk to Petchaburi MRT and there is a lift if needed. Take MRT to Lumphini Park. It is a bit of a walk from Lumphini Park to Conrad so I would take a tuktuk or taxi for that bit.

When departing BKK, I just take a taxi from flat to airport.

I find the traffic too infuriatingly gridlocked to ever consider a taxi into town from airport unless arriving late at night. I travel with checked baggage more often than not too, but one can just wheel it along on route above so is no hassle.