Jordaan Region of Amsterdam? Also Itinerary Suggestions for Bike Trips

You should see the charming Jordan neighborhood when visiting Amsterdam. I would not recommend taking a bike tour in the city, perhaps out in the countryside. There are so many bikes, a means of transportation for the Dutch, and they ride at very high speeds. Pedestrians need to be fully aware of the bike lanes.

The Jordaan area of Amsterdam is indeed a very charming neighborhood - one of the best places to stay in the city I think.
Bike riding in the city can be a bit daunting until you become familiar (and comfortable with) the local cycling rules of the road. A more pleasant option is to rent bikes near the Centraal Station, take the little (free) pedestrian and bicycle ferry across the river and ride thru the pleasant, and level, poulder country in the Waterland area. Beautiful, dedicated cycling paths make it a pleasure to explore for a day. If you're especially ambitious you can ride up to Monnickendam or Marken for lunch.
You can also ride bikes over to Zaandam to see the windmills at Zaanse Schans - a little touristy but with some terrific photo ops on a nice day. That ride is about 12 miles each way - takes about an hour to get there on dedicated cycling paths. If you're not up for that I think you can also get there via train.
The cycle shops offer good quality bicycles at reasonable prices, as well as an excellent map showing all of the dedicated cycling routes in the vicinity. The map costs a couple of Euros as I recall, and the folks who run the shops are happy to offer advice on the most scenic rides tailored to your interests and ability.

I see from your other posts that you're already experienced cyclists, so I think you'll really enjoy the bicycling culture in Amsterdam.

For something less touristy (it is an understatement to qualify the Zaanse Schans as »a little touristy«: it can be extremely crowded), but no less agreeable go to the region south-east of Amsterdam. Start in Weesp (with two windmills on the river Vecht, south of the town centre), follow the meandering small river Gein to Abcoude (along which you'll find another windmill of Mondriaan fame), continue along the river Holendrecht to Ouderkerk (with a historical Jewish cemetery) and then back to Amsterdam along the river Amstel.
In total some 25 km in an extremely Dutch landscape and nice historical towns along quiet country roads, guaranteed without coach parties or other tourist crowds.
The area between central Amsterdam and Weesp is not attractive. Take the train. After rush hour (09.00) you can put your bicycles on the train with a bicycle ticket of around EUR 6.

Biking in AMS is one of our favorite things. Yes its daunting, and Id only suggest it for experienced cyclists. My kids started riding there in their early teens. We have never done a bike tour - not sure what those entail. There are several Youtube videos about biking in AMS if you want to see what its like.
The Jordaan is really nice. What's the concern? It may also be more expensive because its desirable (even for residents). The canal rings are all nice (so you aren't limited to the Jordaan) and if you do rent bikes, you can get from one end of the city to the other in 15 minutes, which really opens up site- seeing and where you stay. Staying in more central AMS, imo, is more touristy and grungy. More partying, more gritty. Typical city stuff. The canal rings are more... cute? Still crowded. AMS is crowded. We also rode bikes out along the Amstel river (RS has direction in his book, but honestly, all you have to do is find the Amstel, get on a path next to it and stay on that path! ;) ). 10-25 minutes out of the city and you are with cows. It situates AMS nicely in context (or take the ride Tom from Leiden describes)

Yes, stay in the Jordaan. It's perfectly safe and within walking distance of central Amsterdam. It's very upscale--think Brooklyn Heights.