Spending two nights in Narita and using the day inbetween to visit either Kamakura or Mt. Fuji doesn't make any sense. You have to cross Tokyo to get to either of those places. Just because you have enough points for (presumably) the Hilton Narita doesn't make it a good idea.

If cost is the issue there are plenty of business hotels in Tokyo with reasonable rates. Especially if you're traveling solo. If cost is really the issue, the Asakusa/Kuramae area has some nice hostels with private rooms available for very low rates.

Just go to Tokyo as soon as you arrive.