Okay given the short time you have I have stayed at the Tokyu Excel narita a number of times which apparently has rebranded to Mystays - I have found it a good deal AND they have an indoor heated pool which can be very pleasant (can't access if you have tattoos and must use a hair cap -which IIRC they'll lend you either lend for free or small charge - I bring my own)
I would take the free shuttle to hotel and then free shuttle from hotel to Narita town - find the walking street which is lined with food shops, bars and leads along a winding path to a temple. Stop in to the tourist place (about half way) - they have a small museum in the back (I had passed it many times before realizing it had free interesting stuff).
If you're not squemish there is a ?famous restaurant serving eel where the eels are killed out front and prepared for cooking (altho I'm not sure they'd still be doing that in late afternnon). Alternatively to cut down on transit time and with no luggage you could take shuttle (I think circle shuttle does this - check online) and then go to the hotel (check with them about shuttle time and location!)
Then I'd take the shuttle to Aeon mall (you could go back to the hotel and catch a free shuttle from there - but the timing may not work out). There is a "circle" bus which cost 1 or 200 yen. At Aeon mall there are LOTS of restaurants as well as a food court - in addition you can walk to the main road where there are a number of small restaurants including a 100 yen sushi place (pretty good and you can even order from a screen and the stuff will come out and stop in front of you!) Mostly local people (when I've been there I think I was the only non Japanese there) - it's very popular so there can be a bit of a wait but it seems to go quickly)
Hint - the mYstays is a 5 minute walk from the Hilton so you could actually take a Hilton (free) shuttle as well if the time works out okay and just walk 5 minutes.
If it's really cold you could just go to the Aeon mall and skip the walking street There's also a large Daiso store at the mall where you can see some amazing stuff for 100 yen if that interests you.