I use Skype for pleasure. The service is useless for business but not because Skype is bad - it's because the bandwidth the service provider (Claro Codetel) gives me in Constanza is awful! The connection quality is also bad so I expect o lose my connection at least 3 times per call.
However, to answer the question about "computer centres", aka cyber cafes. My experience is that they do not have Skype. Most individual drop-in users wouldn't be familiar with Skype and using it is made more difficult as I think Skype has no Spanish version(?). (Yes, I know it's easy anyway - but possibly not if you've never used it and there are no Spanish instructions.)
However, if you were dialling a non-Skyped PC from the USA, it may becheap and probably cheaper to buy a cheap phone card and dial phone to phone (it should make no difference if it's landline or mobile at either end). Check the prices before buying the card. I don't believe Skype can beat phonecards - though it might be different in the USA.
The expense of using Skype to a Mobile Phone can arise because there are sometimes different rates for calling landlines or mobile phones. When there are different rates, calls to mobile phones are always the most expensive!
And sorry to add it but I can't help thinking - if your daughter has a PC/Laptop and the boy (or boys?) here doesn't, they're in different economic brackets so be careful - the odds are stacked against this being an affair of the heart (for the Dominicano) - the opportunity to escape to greener pastures will be a massive temptation. Most important question is probably - how many children has he with how many girlfriends! More than 1, walk away!
Good luck!