I travel to Costa Rica fairly often, and have many friends living there (American ex-pats). I have also done an appreciable amount of fishing in CR, both deep sea and inland (eg., tarpon).
Offshore fishing in CR is, in my experience, hit-and-miss. The most popular fishing destination is propably Quepos. Flamingo, in Guanacaste Province, is sometimes okay, though a much longer drive from San Jose'.
If you like, send me a pm and I'll give contact information on one of my friends who lives in CR and arranges fishing charters. If nothing else, he'll be be able to tell you where the fishing is likely to be good in April.