I've spent a fair amount of time in Amsterdam and have some good "non touristy" places. Renting bikes is the best way to get around. Most bike rental companies have advertising all over them and scream "I'm a tourist" We always get "incognito" bikes that blend in with the bikes the locals ride such as This Place or This Place-We usually rent here Check out Vondel Park, sorta Amsterdams Central Park but not nearly as big. Go have a beer at 'T Blauwe Theehuis (The Blue Tea House) in the park. It sits behind some trees and is hard to see if you aren't looking for it. Tons of multilevel outdoor seating and great people watching. Another thing we like to do is get takeout pizza at Da Portare Pizza. We sit on the edge of the canal right out front, grab a beer from the bar next door....sneak it out...and watch the party boats cruise by. Just around the corner is an all dutch beer cafe Arendsnest that has a handful of tables out on the canal.
There is a neighborhood called The Pijp that not many tourists make it out to. Lots of cafes and restaurants in this area. Off on a side street is a great thai place Siriphon run by a thai family. Really good food.
Another funky area to check out is IJ Noord (north). It is across the IJ river and you can take the free ferries that leave from behind Central Station to get there. There are 3 or 4 different ferries that take you to different spots. The Westerdoksdijk ferry is the best one to take.MTV Europe is over there and some other funky, creative type businesses. There are some old giant ship building warehouses that are now artist studios. You can go in and just walk around and check out the wierd art. Noodrlicht cafeis our favorite spot to have a beer and sit outside on the water looking back at amsterdam. It is a funky, hippy spot but there are some cafes over there that looked like they had normal people hanging out.
I'm a craft beer guy so I hit places like Gollem cafe. They have 2 or 3 locations but the one on Raamsteeg is in old town/ central amsterdam and is a cool old bar. The have all sorts of hard to get belgian beers including Westvleteren....which costs between $15-20 but worth it if you like belgian beers. Another great place is a local brewery Brouwerij 't IJ that has a tap house/ beer garden underneath a giant windmill. There are several street markets around amsterdam. Albert Cuyp Marktis the big one and worth checking out. Grab a Stroopwafels or a smoked herring if you're man enough and walk around.