We were booking a room in Dubrovnik and the lady wants a deposit of 80 euro or 600 Kuna to reserve the room sent by Western Union. I did a price check on Western Union and 600 Kuna was $118 + $22 Western Union fee = $142. Is this typical? The room we are booking is 56 euro a night for 2 nights. This is a B&B. I am tempted to just drive into town and try to book a room. However, we are driving, so we will not be in an area near the train station where people are soliciting rooms.

You could send her an international draft by mail in euros or Kuna for about $5.00.

Yes it's typical in Dubrovnik.
There is no train station in Dubrovnik! There is a bus terminus and ferry dock where people may offer rooms but I didn't see any last year.
When is this for? When high summer is over you will probably be able to turn up and find somewhere easily enough.

We are going to be there 9/21 & 9/22/09. We could just take a chance and see if she has a room open when we get there since this is a Monday and a Tuesday.

Most local apartment owners require a deposit be paid in advance and it is generally legitimate, but I have heard stories of travelers arriving to find no apartment. I usually feel more comfortable booking with an agency that takes credit cards for the deposit like www.DubrovnikApartmentSource.com. At least if you have a problem with the apartment, you have an agency to complain to (and demand satisfaction from).

I had the same issue planning my trip to Croatia in September. After I confirmed availability, I'd explain to the owner the expense of sending a deposit and offer to send a check in US dollars. In every case they waived the deposit. Now my trip is coming up; we'll see if they honor my reservation.