I'll give you a few places to eat that are relatively easy access from downtown.
Donde Carlos (Los Yoses) Argentinian style steak
Hotel Grano de Oro (Paseo deColon) international cuisine, nice place
Machu Pichu (Paseo Colon) good Peruvian food, local favorite
Park Cafe (Sabana Norte) British chef who serves an interesting fusion menu
Plaza Itzkazu (Escazu) strip mall with a variety of restaurants including a Hooters and an Outback. I would recommend the Peruvian place (Chancay), Italian (Tutti Li) or Cuban (La GuaGua).
La Cascada (Escazu) traditional CR steak place, the baby beef is pretty good. The nearby Novillo Alegre also has excellent steaks.
There's also a few places in Barrio Amon area that are worth looking into (Bakea?). The News Cafe at the Presidente is pretty good as well.
A good day trip is heading out to Poas or Irazu volcano...you'll get a great idea of the countryside on the drive. Leave early in the morning so you can see the crater and avoid afternoon rains.