You are right. I have just checked it and it's very close. I haven't realized it before even though I'm from the Eastern part of Slovakia so I could have visited Romania so many times before :)
It looks like a nice place close to the shore. I've heard a lot about Constanca when I was in Bucharest and Tulcea seems to be very close to that place.
I will definitely let you know if we would ever be there. I just hope you won't be cycling somewhere else at that time :)