I stayed at a B&B in a residential neighborhood several blocks beyond the outermost canal, on a small side street that ended at the Vondelpark. I loved staying there; it was quiet at night, I could walk into town if I wanted to, but I could also catch a tram half a block away and be into the center of town in ten minutes. Amsterdam (and the Netherlands as a whole, for that matter) is very easy to get around via public transportation, so you don't need to stay right in the center of the action in order to be close to everything.
The suggestion above of an apartment near the Anne Frank House also sounds lovely; that's a wonderful neighborhood. And speaking of the Anne Frank House, if you want to go, I would suggest buying tickets as soon as they become available; I think they start selling them two months in advance.
I didn't go on any organized bike tours, but you can do a lot of riding in the different neighborhoods of the city. There are far more bikes than cars in Amsterdam, and there are bike lanes almost everywhere.
Day trips: I recommend Haarlem, Zaanse Schans (touristy but still worth it to see the windmills), and Marken (Rick Steves's book suggests a tour combining it with Volendam and Edam). You'll probably also want to go to Keukenhoff and Aalsmeer; I didn't go during my July visit, but you'll be there during tulip season. Rick suggests some other day trips that sound great, but I was enjoying Amsterdam itself too much to want to venture out of the city any more than that.
