I was there this summer with my 16 year old DD, and felt perfectly safe!
We did walk out of the port area to the Hard Rock to catch a taxi (saved $1 per person, if I recall correctly). You can also catch a taxi right by the port area. If you email Steve at the Tropicante (Google for his website, email link on it), he will give you all the info you need on getting to Tropicante from port.
DD and I actually like the walk to the Hard Rock. We did feel safe, and though the area does look run down by American standards, it is just very ocean worn. You walk under a long arbor filled with beautiful flowers on all sides, and we even met a Gecko that was just hanging out on a piece of wood! Since we have no fear of lizards, we got right up and admired him, taking lots of pictures, since we don't see Geckos on our walk around town at home!
There is also a store just before you get to the Hard Rock, on the other side of the street. On the way back, we stopped here for souvenirs. The prices were better than in the port area, and there were many unique, Made in Mexico items.
When the taxi drops you in Mahahual, you will walk between buildings (the main road is behind the buildings on the beach, no cars on the beach road). We made a left, and saw the sign for Tropicante right away. The taxi driver was very nice, and escorted us to the entrance. I don't know if they all do this, but I was attempting to speak in Spanish, so maybe he just liked my attempt and felt "fatherly" towards two females traveling alone? Don't know, but he was very nice.
I do not worry at all in Mahahual, beyond my normal awareness of surrounding wherever I travel. I feel more at ease there than in the Bahamas, or even in Cancun.
And we only stayed about 3.5 hours. Fantasy is hardly in port for any length of time, but DD and found 3.5 hours to be plenty for soaking sun, playing in water, eating and drinking time. Oh, and they do serve 16 year olds alcohol. I am from Europe, and am fine with DD trying a drink with me, so I don't mind, but others might feel offended, so just know that if you have at teen, they may be offered something. In Mexico, this is just how it is. We shared one strawberry Daiquiri, it was tasty, and the nachos were fantastic!
If I ever end up in Costa Maya again, we will definitely head for Tropicante. Really a nice, real Mexico experience!