You might consider browsing the dedicated sites, such as chrono24, which sell used watches.

When people desire cheap watches I tend to recommend some of the old USSR pieces, they were made in the millions and so they're very available, and they're cheap and reliable too.

These days there are new options available, so you might consider searching for things made by Vostok, or similar.

(Half my watch collection is Swiss-made, the other half is mostly Soviet vintage pieces.)

I guess it depends on what affordable means to you. You can find quite a few Orient watches without date at really reasonable prices, a couple of Timex too. If you're willing to spend a bit more you can also get various no-date Hamilton.

Depends on your definition of expensive, but you can find used Hamilton khaki field watches without date complications in the $100-$1000 range. Even some new ones are listed under $1k:

https://www.hamiltonwatch.com/en-us/collection/khaki-field.h...

FWIW, a $100-$500 Hamilton automatic field watch is a good deal, and not "expensive" by any objective measure.