I want to install a utility sink in a garage where there is an existing unused washer/dryer hook-up. Can I connect the sink directly to the unused washer drain? This seems like it should be pretty simple, am I missing something? Thank you.

I don't see why not. Just remember that the height of the existing washer drain pipe opening is probably higher than the bottom of the utility sink. So if you just ran a hose from the bottom of the sink into the drain the sink would not drain properly. Also there should be a trap under the sink that lowers the height the drain should be as well. You may have to cut the sheetrock in front of the drain pipe to get to where you can then cut the drain pipe to fit. You should also be able to use the existing hot and cold water taps to supply your sink.