I've spent a fair amount of time in the Netherlands over the years, on business, and so have some reccs (concentrating on outside of Amsterdam, since there is plenty of info on what to do/see IN Amsterdam).
Since you said you'd be in Leiden, you should check out the museum of antiquities that's associated with the university. There is also an old stone windmill with house on the first floor, that belonged to Rembrandt's family - he lived there as a kid. Well worth a quick visit.
Although the bikes in town or in the cities are mostly your basic commuter bikes, there is a lot of road bike use on the weekends, out in the countryside. You can definitely find road bikes to rent for some longer country-side rides.
An area that makes for some good road cycling is the area to the north and east of Amsterdam, that runs along the IJselmeer (used to be called the Zuider See). (As an aside, one key tip to pronouncing Dutch is that the ij combo is really a single letter, denoting a long I sound. Which is why both the I and the J in IJselmeer are both capitalized. Another tip is ui is pronounced like au (So Haus in German, and Huis in Dutch, both mean house, and all three are pronounced the same. For the same reason, Braun in German and Bruin in Dutch are both brown, and pronounced at least almost the same.))
The towns along the IJselmeer include Edam (known for its cheese), Volendam, and Marken, all of which are pretty quaint. The latter two still have a lot of traditional Dutch small-town life. Closer in to Amsterdam, but also to the northeast, is the Zaanse Schans, sort of a historic park consisting of a bunch of old wooden windmills, restored homes, businesses, etc. Another interesting site is Muiden, which has a pretty cool old castle.
Check out this link:
I used to stay in Hilversum a lot, and close to it is a pretty cool old walled town, Naarden, with star-shaped city walls/fortifications, a moat, etc. It has a very tall old church, and you can pay small fee and go up into the bell tower (very Quasimodo-like, with narrow wooden stairs, the exposed bells, etc.), for a great view.
Other towns that are down past Leiden include Delfft (the famous hand-painted pottery), and Gouda (another cheese town). Plus the big tulip fields and the botanical gardens (Kuekenhof Gardens?) are worth a stop
If you can get all the way down to the Hague, that is where the seat of the Netherlands govt. is - also there is a pretty nice casino right next to the beach in Scheveningen (sp?), which is basically a district of the Hague.
You need to eat some good pannekuchen (basically pancakes, but really more like crepes, in that there are desert types, as well as regular meal types), as well as other typical Dutch dishes like schnitzels, Varkenshaas (pork tenderoin, basically). And of course some good ice cream, usually vanilla ice cream with whipped cream, and some other topping. (IJs met shlag, plus whatever the topping is...) I really like IJs met Advocaat, which is an egg liqueur that is bright yellow. Don't know why the name sounds like "lawyer"...)