Introduction
Amsterdam isn't as large as many of the other European capital cities, yet it still has plenty to see and do. I'm not going to try to cover it all but rather just give some tips regarding things I like or places I think shouldn't be missed if you've got only a little time here. The major tourist attractions are better covered in your guidebook or whatever.

One thing about which you might want to know is the free English-language weekly aptly called Amsterdam Weekly. You can pick these up all over town - I know they have them at Club 11, The American Bookstore, my school (ISHSS), often there's one at Cafe Latei, etc. Usually has a good deal of info on music, art, and other events (there's usually a lot of cool random stuff going on in town) as well as locally-focused articles.
Bars
There are over 1200 bars in Amsterdam, so whittling down the choices can be overwhelming. Here are a few of my favorites to get you started on the right track.
  • Scharrebier - Rapenburgerplein 1

    My favorite cozy neighborhood bar. This place isn't eye-dropping nor large, but if you want to hang with the locals in a pretty little brown cafe that is run by nice old Dutch guys, always packed, and always has some good Belgian beers on tap then this is your place. I may be biased since it's right around the corner from my place, but I am here at least every other week.

  • Cafe Belgique - Gravenstraat 2

    A great example of the typical Benelux "brown cafe", this bar has a beer menu that gives you the breakdown of all their many varieties. It's very small and usually packed but somehow I often get a table anyway. Very pretty decor and very pretty bartenders, too. :)

  • Het Schuim - Spuistraat 189

    Nice open space with big comfy chairs just around the corner from the Dam. Very interesting mix of patrons, ranging from punker homeless types to businessmen in suits. Also sports interesting Picasso-esque paintings on the walls. Come here if Belgique makes you too clostrophobic.

  • Het Elfde Gebod - Zeedijk 5

    Another nice brown cafe, though I like Belgique a little more. This one has the benefit of being close to the station for people who don't have much time to explore the city and is also very near Chinatown so you can get some good cheap food as well. Many beers, tablecloths made out of carpet, and a jolly old man running the place make it worth checking out.

  • L&B - Korte Leidsedwarsstraat 82-84

    Before I went to this bar I thought I didn't like whiskey. I realized that I just didn't like bad whiskey. They have over 600 varieties with many in the very affordable range and the decor is typical nice brown cafe style with some pillowed benches. The staff is very knowledgeable and willing to give recommendations. A gem in the otherwise touristy Leidseplein area.

  • De Zotte - Raamstraat 29

    Yet another great brown beer cafe that has a great selection, is usually quite busy, and is worth checking out.

  • Soundgarden - Marnixstraat 164-166

    Very cool punker bar with an alternative crowd and a very nice backyard outdoor seating area right on the canal.
Going Out
Amsterdam also has plenty of things to do in the event that drinking good Belgian beer isn't how you want to spend all of your time. Here are a couple things that I think are unique enough that you should try not to miss them while here.
  • Club 11 - Oosterdokskade 3-5

    This is one of the things that I don't think you should miss if you travel to Amsterdam. Club 11 is located on the eleventh floor of an old post office building near the central train station which also houses the Stedelijk Museum, the City Museum which has mostly modern art. The views from the Club are fantastic and you get great looks at both the old city center and the IJ. During the day the space is used as a cafe with good sandwiches. At night it turns into a club featuring a big dance floor, projection screens on all the walls with live video art, TV screens and chalkboard walls in the bathrooms, etc. I don't even like techno and I like going there for their dance parties.

  • Bimhuis - Piet Heinkade 3

    The jazz club within the new Muziekgebouw aan 't IJ, this place also has amazing views of Amsterdam and the IJ, though from here you get to see them behind the music stage where you'll get to hear some great live jazz. On Tuesday nights starting at 10pm there's a free jazz improv session where students jam and the quality is usually quite good. Drinks are a bit expensive and the clientelle is a bit prim, but hey, it's a jazz club after all.

  • Occii - Amstelveenseweg 134

    A legalized squat, Occii has many concerts and sometimes hosts acts as big as Don Caballero. Very cool alternative atmosphere and cheap Pilsner Urquell.
Eating Out
Eating out in Amsterdam isn't cheap so I don't do it all that much. Here are a couple recommendations based on my limited experience.
  • Eat Mode - Zeedijk 105-107

    This place has food that ranges from Japanese to Thai and is nice and cheap. Free WiFi and near to Nieuwmarkt.

  • The Bird - Zeedijk 72-74

    Slightly more expensive than Eat Mode but much more flavorful. I've got a soft spot in my heart for spicy Thai and this place has it. There's a snackbar with slightly cheaper food from which you can get takeout or across the street is the sitdown restaurant.

  • Overtoom 301 - Overtoom 301

    A legalized squat which has amazing vegan dinners on Sunday evenings. You must call ahead and reserve your meals a few hours in advance - you'll be out of luck if you try to just show up. Also shows movies (mostly on Sundays) and has lots of cool concerts. Check out the website for a current listing.

  • Pretoriusstraat 28 - Pretoriusstraat 28

    A squat out on the near east side with great vegan dinners on Mondays and Thursdays. Again, call ahead to reserve a place. Also has a free store goods swap on Saturdays.
Cafes
These are cafes rather than cofeeshops, i.e. places to grab a cup of coffee and read or study or do whatever it is that you do in a cafe. Most of them turn into bars at night (the Dutch word for bar is in fact cafe).
  • Cafe Latei - Zeedijk 143

    Most cafes in Amsterdam are actually what Americans would call bars but this one is a true coffee house. The decor is retro, the food is good and cheap, and best of all everything in the place is for sale, including ceiling lamps, chairs, shoes, etc. A neat little place to study or meet travelers and locals.

  • Twee Klaveren - De Clercqstraat 136

    Self-labeled bridge and chess cafe, this is my favorite place to get my fix of game playing. Yes, I like to play games.