I must agree with Traylor Park, Mia2EWR and (dare I say it?) Berk here.
In my opinion, this is not the time to go to C.R. and get laid. At best, C.R. would be a temporary and in the end, ineffective bandaid for your sorrows. At worst, the pain you're feeling now could ruin your enjoyment of the trip. Get your affairs in order, mentally, financially and most importantly emotionally before you jump into someone new.
T.P.'s advice is golden, point by point. No, the lady does not love you anymore, regardless of what she might have said. She will always care for you, if for no other reason than that you are the father of your k*ds...but your relationship is dead and cannot be resurrected.
My advice for what it's worth: Get yourself as healthy as possible in all respects. Then, when you're ready, Costa Rica will be ready for you.
I sympathize with you, and I agree with others here who have suggested a change in your screen name. You're not an idiot simply because your wife cheated on you. You're a bright guy who is going through some nasty shit right now, but like a kidney stone...this pain too shall pass.
My best wishes to you.
Paul