My choice would be Sutton in the Eastern Townships--a lovely town and a good base for exploring that part of Québec.

Stay at the Vert le Mont B&B.

The Eastern Townships would be my choice, too. My husband and I like to go up to that region for day trips from northern Vermont.
We enjoy visiting the abbey of St. Benoit du Lac in a beautiful setting on Lake Memphremagog. The monks conduct several services a day with Gregorian chant.

There is a wine route, and it might be fun to visit one of the vineyards. Restaurant Le Tire-Bouchon de l'Orpailleur in Dunham is good if you want to stop to eat, and it has a small exhibit about wine making. We have also enjoyed eating in Knowlton where the local specialty is duck

You can search for Eastern Townships and find some trip reports. This is the link to the tourist web site which has suggested routes.
http://www.easterntownships.org/

If you and your sister have passports, you should have no trouble at the borders. We often cross at small border crossings. They are more inclined to pop the hood and check on what we have brought back than they would be at busier places.

I will second the above recommendations - the wine route is lots of fun, and the abbey is beautiful. Another nice town is Magog, which is a small resort town on lake Memphremagog. A little like Burlington, but very French. Bromont and Sutton are also nice small towns that are in ski country. One of the best features of this part of Canada is the amazing network of paved and gravel biking trails - considered the best in the world by many. The major trail known as the Route Verte.
Of course the crown jewels of this part of the world are Montreal and Quebec City, but these would require at least an overnight.
Crossing the border at I-89 or I-91 is a piece of cake - usually a 5 or 10 minute wait. If you cross at I-89, you will notice the landscape changes dramatically once you are in Canada - very flat farmland dotted with tiny villages.

Hi gypsy_grey,

You say you look for things that are "genuinely Quebec (and not American)". I must say, when you get this side of the border, you'll see that things in Quebec really are most genuinely Quebec, which is North American in its own way... but you won't feel as if you're in the United States most places, if that's what you're asking.

Thinking close to the border, I agree that the Eastern Townships is a good choice of where to head. Magog is a great suggestion; I even liked Sherbrooke, a bit industrial on the outskirts, but with a pleasant central area and a Musee des Beaux Arts. Both have a nice walkable core. I also enjoyed Chambly in Monteregie (closer to Montreal) has a fort which is a National Historic Site and definitely worth a look if you like history... there's a number of charming houses and restaurants within walking distance of the fort.

Have fun and do consider a longer visit to Montreal itself at one point.

Best wishes, DAniel

Many of those small towns in Quebec will afford you quite the "not American" sense you seek.

When driving through some of them I was quite in awe of just how striking the local churches tend to be, and I'm sure there is plenty of French culture that will remind you that you're indeed in a "foreign" place.

(the bigger the city/town, the less immersed in French you are likely to be)

Another National Historic Site near Vermont (besides the fort at Chambly mentioned in Daniel William's post) is Fort Lennox on Île aux Noix, in the middle of the Richelieu River. You reach it via a short boat ride. Both it and Chambly are interesting with pleasant natural surroundings.

the older part of Saint-Jean-sur-Richelieu along the water is also quite pleasant, and there are cruises from there to Saint-Ours along the Chambly canal (we have not taken a cruise ourselves)