i agree. sink is horrible. break out the concrete and that sink, and replace them w/something else.
all of these have farm house sinks which would take the place of what you have now.
if you tile on top of that cement, it's going to raise it by at least an inch. You'll have to redo the faucet and you will still have that horrid sink. Plus, you'd have to tile all around the sink, including the front portion. how bad would that look? No,,just rip it out.
why the hesitation over taking it out?
another option, call in a cement floor refinisher and see if he can do anything w/your counter. it would be messy, but perhaps he could grind it a bit and do a diff color. then he could seal it for you.if he could completely redo it so the color is more even and works w/the splash, it might look better. Perhaps he could do an overlay on the sink portion. Or, cut out the sink entirely and put in a new sink. if you did one of the farmhouse sinks in a ceramic, he could cut and finish the cement portion around it.
Can't hurt to ask.
(And Pam, tiled countertops are not unsanitary, at least not the tile itself. It's the grout that gets dirty. they have newer grouts on the market that don't allow germs and grime to build up in the pores. Plus, if you're a clean person, there's no reason why you can't stay on top of keeping the grout clean. you should never cut on the tile, so using cutting boards helps keep them free of yuk. sealing the grout also keeps out yuk)
Q