N'EX to Tokyo station + taxi will work fine. The taxi will probably cost about 1300yen.
One cheapo option with minimal effort would be:
11.42am Keisei Limited Express - departs from Narita Airport Terminal 1
12.45pm Arrive Aoto
Change at Aoto (just walk across the platform IIRC)
12.48pm Keisei Oshiage Line - departs from Aoto
1.13pm Arrive Shinbashi station (Asakusa line)
Then a short walk to Conrad
Are Conrad guests interested in cheapo options?