Limón is not the best place to wander around on your own; but you should be fine taking a ship excursion into the interior. I have not been to Colón, but here again I think you would do best staying with the ship excursions.
I should point out that Limón and Colón are both seaports but are not islands.
STRONGLY suggest doing ship excursions in Limon.. I have a freind that went there on a cruise and was robbed 10 min after leaving the ship..Mostly I dont worrie when we go out anywhere else,but here I would.. Be safe..
Belize is ok if you stay in the port gated area. Outside the gate i am not sure..There seems to be plenty of Americans that vacation there other than cruisers so you may be fine.Roatan is fine,Carnival has there own port area there but you are on a island and not the main country.Out of all the ports I have been to Belize and Ocho Rios are the only ones I have been worried about but I would go again.. But it does not matter where you are You must be aware of where you are.Who is around you. And NEVER leave the main shopping area, main road.. remember that goes for here in the U.S.