I know Montreal very well but I'm afraid I can't be quite as helpful about Quebec City. I've only been there a couple of times so I can't offer too many specific recommendations. It is stunningly beautiful and is unlike anywhere else this side of the Atlantic. It's an old walled city and feels more European than North American.
I can think of two Hollywood movies that were filmed there. One is 'Catch Me If You Can' (2002) with Tom Hanks and Leonardo DiCaprio where it doubles as the French city of Montrichard. Alfred Hitchcock filmed his move 'I Confess" (1953) there and it was set in Quebec City as well. The city wasn't standing in for some other location. If you're a movie fan like I am, you should track down the Canadian film 'Le Confessional' (1995) directed by Robert Lepage which is largely about the affect the filming of 'I Confess' had on the city. It's a brilliant film.
There will be lots of tourists, but it's a big enough place that it won't be overwhelming. They speak French almost exclusively, unlike Montreal where virtually everyone is bilingual and English is as common as French. I wish I could suggest a list of specific things to do and see, but on our couple of visits, we spent most of our time just walking around taking in the sites. It is a feast for the eyes. While the greater city spreads out, covering a huge area, the old walled city is really manageable on foot and in fact that's the best way to see it. Driving in the old city is challenging. There are countless restaurants and bars, and plenty of outdoor patios. One excellent and very interesting restaurant is 'Aux Anciens Canadiens' which is located in the oldest building in the city dating from 1675 and they offer authentic Quebecois food.
I don't know if you're interested in churches or not, but the whole province of Quebec has outstanding churches and cathedrals. In Quebec City, the big one is Notre Dame de Quebec Basilica-Cathedral. Another interesting but small church is St. Andrew's which is the oldest Presbyterian Church in Canada (it goes back to the mid 1700's) and is English speaking. It's right in the centre of the Old City and is well worth taking a peek inside it happens to be unlocked. Another interesting one is the Cathedral of the Holy Trinity which is Anglican (Episcopalian.) It's the oldest Anglican church anywhere in the world outside the British Isles.
If you're interested in organ music (I know this one is probably a stretch! - there are very few of us who actually are) there are almost certain to be organ concerts at various locations throughout the city. One of the finest organ builders in the world, Casavant Freres is located in St. Hyacinthe, Quebec and their organs are featured prominently throughout the province.
One thing you really should be sure to do though is visit the Plains of Abraham, which is the site of the most famous battle in Canadian history which was arguably the pivotal event in our history. You'll be able to find plenty of information about the Battle of the Plains of Abraham online.
I don't know if any of that is helpful (or even interesting) but if not I'm sure you will be able to find other things online and maybe someone with more and better experience can add something too.
In any case, I really hope you have a great visit to Quebec!
David