We are flying into Brussels for 10 days in the region. We may visit Germany or The Netherlands or both. To travel by train is it much more expensive to just wait until we get there and decide where we want to go? We like to go with the flow but we are willing to plan a little better if it would save us a lot of money. I've never traveled in Europe before. Thanks!!
"international trains will be significantly cheaper if booked in advance"
I'm repeating Philip's reply with bold emphasis added. To see what I mean, use the websites he listed, then look at prices for tomorrow vs prices for a few months from now.
To go from Belgium to the Netherlands you can take local trains that won't be more expensive bought at the last minute, but these can be much slower and require more changes. If you have more time than money, this works; if you're taking a day trip, it may not.