Where to go before river cruise

Your interests?

Have you been to Belgium? Both Brussels and Bruges are beautiful with lots of things to do.

We would like to stay away from big cities. Like traditional and cultural

Close to Amsterdam are Haarlem, Delft, Utrecht, Leiden, Volendam, Gouda, and more

Bruges and Ghent

Yes....Amsterdam has always been on my one and done list. There are many other alternatives in the Netherlands but I don't understand why with an entire week you wouldn't plan for something like Paris? A week gives plenty of time to plan time elsewhere.
I also like Brugge, but it's a two-day destination for me. Add Ghent, ok, two more days, you still need at least two or three more days. Fly into Paris and make your way to your cruise from there.
Don't overlook the UK as another option. You can arrive at Ostend and travel from there....
So many options, all not Amsterdam.

We spent a wonderful week in Leiden. It is on the train line so would be easy to visit.

It would be useful to know the month of the year, and whether you have already been to (or if the cruise includes) Keukenhof. Did you mean other places flying-into-Amsterdam? After all, we don't know good cities to fly to from your (secret) home area.

I've been to Amsterdam at least four times, and I haven't repeated many sights (except pancake houses ... ). There's plenty of culture and tradition in Amsterdam; Have you been to a concert at the Concertgebouw? Have you been on a tour of canal-house gardens? Have you been to Haarlem?

As noted, many small cities are within an hour, on unreserved, inexpensive train lines. I've been to Delft twice from Amsterdam, and it abuts Den Haag, an equally historic/cultural city.

If the idea is to stick around Amsterdam to burn those extra days, that is certainly possible, Hoorn, Harlem, all interesting and an easy train ride away. There is no doubt that you can find enough to do there. Keukenhof is on par with Singapore Gardens, maybe even more impressive because of the way that bulbs are organized.
That said, given the choice of a bit of herring, a cheese sandwich and a Becks, I'll go for a good Triple and a Carbonnades flamandes, or in Paris, a nice dinner at almost any Bistro, a perfect steak and Bordeux.....
A few days in Amsterdam are plenty and they really don't want you there anyway.

I agree with Tim that you should look at what transatlantic flights work best for you. You can connect to Amsterdam by air or rail from just about anywhere.