I can hear water dripping into the tub, not sure just where it comes from...
We checked the drainage hoses for any blockages, as we first noticed water in the tub after washing cycle, and thought it wasn't draing, but everything is good in that department. But now that I hear a steady drip, drip, drip, I'm wondering what to do next?

Sometimes water inlet valves (especially the cold water valve) and especially if you have well water, can become partially clogged with silt, dirt and other debris, and you can shut off your water, remove hoses, remove valve log, then rinse it well if debris is found, also probe with a toothpick or something to remove any sediment you see in there, rinse again and then re-install valve log and see if it still leaks.

My guess is something is preventing it from closing all the way, thus your little leak.

This is the cheapest way to remedy situation. I would not purchase a new valve without attempting to clear first. Unless you just want a new one.