Our kitchen is presently under construction, but I have a 4-drawer base cabinet to the left of the sink for towels, my DW is just beyond this cabinet (I have a corner sink base so DW couldn't be next to the sink). I also have a trash compactor to the right of my sink with a bar-style handle that could be used to hold a towel. In my old kitchen I had a bar inside my sink cabinet door to hold the towel I am using.

I keep my clean towels in a drawer, along with potholders and placemats, trivets, etc. Maybe I am fortunate to have the extra drawer space?

My in use dishtowel hangs on a hook on the inside of my sink cabinet door. My DW also sits to the side of my sink. I have two doors in my sink base, one side holds the trash can and I use the other door for hanging my towel.

I don't use a dishcloth, I use a sponge and it sits in a ceramic holder on the counter on the edge of the sink base. When we get our remodel done and I get my new undermount sink, I will probably find a new spot for the sponge. I have a tip out under the sink, but I think it would get musty being put away wet?? We'll see.

also, check out this thread. some great pics of how others hang their towels

Here is a link that might be useful: Where do you hang your cloth hand towels?