do small towns in belgium with pop under 2000 people have inns or b@b?

Question

and do you know the names of any of these towns

Answer 1

Yes there are a lot.
One increasingly successful formula is the "chambres d'hôtes". That means that people have one or two rooms in their own house that they rent. Usually it is only in charming places and rural areas. I have tried and really enjoyed the not commercial side of this option.

Try websites below, maybe choose first the region of your preference.

Hope this helps

Answer 2

In Antwerp their a few B+B but it's more then 2000 people.
You won't find that here so much, here are more hotels.
Don't think it's the same here then in UK, best check Rustic info Belgium, but beware that the distance can be big from distentions.