Yes there is a free shuttle that runs between the HI (AKA Tobu Narita) but only once every 30 mins or so. Trip takes about 20 minutes or so (you need to go through a security check - which means that the police will stop all traffic, board the bus and check everyone's documents).

The hotel itself is OK. Certainly good value for money.

To make the most out of your last day in Japan, I'd strongly suggest getting a room within Narita town itself.
Pricewise, Comfort Inn is a good deal for one person: http://www.choicehotels.com/ires/en-...fo?hotel=JP026 (just under 6,000 yen)
for two people, I'd advise staying at the Mercure Narita (usually 9,000yen through www.mytrip.net/en)
Getting to the HI in the evening is a pain in the butt, once you're there, there's nothing to do - just a convenience store. And it'll take at least 30 minutes to get from the hotel to the airport.

By staying at Narita town, you'll be checking in just minutes after the train gets there. Plenty to do in the evening, lots of nice restaurants, nightlife if you want it. In the morning, you can have a nice stroll around the temple gardens (the temple is a major draw in its own right), check out, and if you're aware of the train timetable you can leave the hotel and be inside the airport within ten minutes. Works for me!