Taxi from Haneda airport to the Conrad hotel might be marginally faster than the Monorail + Taxi route that ksandness suggested and somewhat more comfortable. However, I don't think it's worth paying $60-$80 (my guess) more for just a few minutes in saved time.

There's a dedicated taxi rank at Hamamatsu Station. Follow signs for taxis, when you emerge from the building it's on the right side - in a little alleyway between the Monorail station and the JR tracks.