In a week, I personally wouldn't go to more than 2 spots. When Google Maps / Waze says that it's 2 hours and 23 minutes to drive the 70 miles between SJO airport and La Fortuna, and you think that's crazy slow, it's right, you're wrong 🙂
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https://www.google.com/maps/dir/Juan+Santamar%C3%ADa+International+Airport,+Alajuela+Province,+Alajuela,+Costa+Rica/Alajuela+Province,+La+Fortuna,+Costa+Rica/@10.2200425,-84.5518231,10z/data%3D%213m1%214b1%214m14%214m13%211m5%211m1%211s0x8fa0f9c450507873:0xb27b62220e3f31a4%212m2%211d-84.2040642%212d9.9980013%211m5%211m1%211s0x8fa00c890660e999:0x69e3a87bd2572ce6%212m2%211d-84.6426806%212d10.4678335%213e0[https://www.google.com/maps/dir/Juan+Santamar%C3%ADa+International+Airport,+Alajuela+Province,+Alajuela,+Costa+Rica/Alajuela+Province,+La+Fortuna,+Costa+Rica/@10.2200425,-84.5518231,10z/data=!3m1!4b1!4m14!4m13!1m5!1m1!1s0x8fa0f9c450507873:0xb27b62220e3f31a4!2m2!1d-84.2040642!2d9.9980013!1m5!1m1!1s0x8fa00c890660e999:0x69e3a87bd2572ce6!2m2!1d-84.6426806!2d10.4678335!3e0]
* Skip San Jose. There are some cool things there, but probably not the type of stuff that you are looking for with your group.
* Go to a beach town, and a mountain town
Like Samara / La Fortuna, Esterillos Oeste / Monteverde, or Tamarindo / San Gerardo de Dota
Most beach town also have other beaches/towns nearby, easy visits. Most have waterfalls in the vicinity. Mountain towns are a bit more remote, lots of hiking, nature stuff, hanging bridges, etc.
Go surfing, visit waterfalls, do white-water rafting, butterfly gardens, horseback rides, etc...
* May/June is starting the rainy season, not a big deal, but the more you move towards Guanacaste (NW peninsula), the less rain you'll have. Even in the highlands, or the Central Pacific, might rain in the afternoon at 1pm, but that's about it. In the Caribbean side, rains year around, would avoid.
* If you want to go to a beach in Guanacaste (NW peninsula), just fly into Liberia airport (LIR) and rent a car there, avoiding San Jose all together.
Personally, I LOVED the Dominical/Uvita area that we just got back from... Kind of remote, but mountains on top of the beach, tons of very cool waterfalls, great beginner surfing for my kids.