The best waterproof boots for long walks on rough terrain include the Merrell Moab 3 Mid Waterproof, known for its durability and comfort, and the Salomon X Ultra 5 GTX, which offers excellent traction and stability. Both options cost about $180, and are designed to keep your feet dry while providing support on challenging trails.
If price is an issue, then check out the Free Soldier waterproof boots offered on Amazon for a bit over $50, or Amazon's other offerings.
The biggest problem is where to buy the boots, because it is best to get them properly fitted with the stockings (2 pair) you intend to wear. I bought some Merrell Gore-tex boots when I moved to Costa Rica. IIRC, I bought them at REI, and the sales persons who help my wife and me really knew their stuff about long walk backpacking in rough terrain. The boots worked well for hiking in volcano and rain forest parks.