Hi Bogdan,
I'm also a big fan of Pedasi. It's my favorite place in Panama. It's one of the friendliest towns here. And when I say friendly, I mean the local Panamanians living there and the foreigners. What I found to be so cool about Pedasi is that it's not all Americans like some of the other expat-heavy destinations. In Pedasi you'll find people from the U.S., Canada, U.K., Australia, Spain, France, Israel, etc. It's awesome.
With the new airport opening up there and the new hospital on its way, it's probably one of the most realistic living options outside of Panama City, Coronado, David, and Boquete. For being so small, it actually has a lot to offer, and with it's close proximity to Las Tablas and Chitre, you should be able to easily find anything you can't get in town. One restaurant owner told me he gets his meat from a butcher in Las Tablas. One other foreigner said she makes the 45minute-1 hour trip to Chitre to visit the mall and catch a movie (it's a small 4 screen movie theater though).
Mikkel gave you tons of great info, all of it true. The only thing I wanted to touch on is that if you're going to take a bus from Albrook to Pedasi, you will need to take it to Las Tablas, like Mikkel said, but from that point you don't have to take a taxi. You certainly can, but it might cost a little bit since Pedasi is a good 30 minute drive from Las Tablas. If you leave the bus station and either walk or take a taxi over to the main street in Las Tablas, you'll find small Coaster buses parked across from the first supermarket in town (can't remember the name, but it's closer than Super Carne). These Coaster buses will only cost $2.40 each way. You might have to wait for a few other passengers to get dropped off along the way, but it has to be a lot cheaper than paying for a taxi.
I'd follow Mikkel's advice and contact someone who lives in Pedasi before going, just to make sure you don't miss anything. I had a friendly Panamanian woman take me around and I got to see the port built by the Japanese, where a small fishing boat was donated to the people of the area, I was taken to Playa Venao (which is technically outside of Pedasi, but still a big part of life there, as many Saturday evenings people come in on buses to party until the sun comes up), and I was taken out to meet a boat captain who will take you over to the beautiful Isla Iguana for $60 per boat-full. So if you round up five of your friends it would be a pretty cheap trip over to the island.
I can't wait to go back to Pedasi. I'll be headed back soon as I plan to write about it in my new site that should be launching right around mid-April at www.panamaforreal.com. Right now, the site is under construction, but if you want to read more about random Panama facts, check out my blog at www.thestayathomegringo.blogspot.com.
Whatever you do, definitely find time to take a trip out to Pedasi. Make sure you're there on a Tuesday or Friday night so you can head over to Smiley's and catch the live cover band and order one of their gigantic pitchers of sangria.
Chris