Tom,
Unless you stay at a small hotel outside of town, you will have people around. There are a few hotels close to the train station, but don't be limited by that. Keep in mind that Monterosso consists of an "old town" and a "new town", there are hotels in both parts and it's very easy to get around on foot.
A few hotels that you could consider are.....
- Hotel Villa Steno (old town - not close to the station but my favourite - I normally take a taxi from the station)
- Hotel Pasquale (old town - very easy to get to)
- Hotel Villa Adriana (new town along the road into town - easy to get to)
Those are all within walking distance to numerous restaurants. One of the favourite restaurants with many here is Cantina di Miky which is right on the main street close to the station.
I don't know which hotels and restaurants will still be open at that time of year, but I suspect that most will be open. For more suggestions, have a look at the RS Italy guidebook.