Several cycling sites have good links pages. Rather than reproduce their lists, have a look at these sites.
CTC
Britain's national cyclists' organisation
CTC Scotland
The Scottish 'Region' of CTC
SPOKES
Lothian Cycle Campaign - very good links page arranged in useful categories
Cycling Scotland A team of experts in various fields (training, health, transport, cycling infrastructure, etc.) each also with a geographical remit is there to help promote cycling throughout Scotland. The project supported by the Scottish Executive.
Scottish Cycling The governing body for cycle sport in Scotland
Sustrans Scotland Sustainable Transport charity, promoting especially cycling and school travel

 

Below is a selection of a few sites which may be of interest to those in Lothian
Mellow Velo An informal group who arrange weekends away, usually using trains to get to the cycling area, and staying in hostel-type accommodation.
Cycling Edinburgh An attempt to record some of the many cycling activities in and around Edinburgh. Plus cycling stories from here and there.
City Cycling Edinburgh CityCyclingEdinburgh is an experiment to see if a new forum for people who cycle in and around Edinburgh (Scotland) is going to be a valuable addition to the web..
Cyclestreets local routeplanning facility
Audax UK long distance cyclists' organisation
the Bike Station It's a community service, bike recycling and workshop. Donate a bike that's not being used and let it help someone else, or offer to help with the reconstruction of donated bikes. More details.....
Edinburgh Bicycle Co-operative one of the biggest bike shop web sites in Europe. Has an online catalogue, up-to-date news on special offers and a good supply of cycle routes. Lots of links to cycle groups and manufacturers
Edinburgh Road Club Emphasis on racing
Edinburgh University Cycling Club A comprehensive site
Fife & Kinross Member Group next-door neighbours
Friends of the Earth (Scotland) latest news on Traffic Reduction Act, green transport campaigns etc.
Go-Bike/Strathclyde Cycle Campaign for the Glasgow and Strathclyde area.
Rough Stuff Fellowship founded in 1955, is a cycling organisation dedicated to the pursuit of cycling on bridleways, byways, drove roads and tracks. The RSF doesn't stage competitive events but its members are dedicated to the enjoyment of off-road cycling on the quieter routes in the UK.
Safe Routes to Schools - Scotland a specialised part of the Sustrans site
First ScotRail no charge for bikes, find which trains in Scotland you need to book on
Scottish Youth Hostel Association detailed information on all of their hostels in Scotland - open to all ages, not just "youths".
The Tandem Club was formed in the UK in 1971 primarily to provide otherwise unobtainable spare parts and technical advice on how to maintain the older machines. This is still an important function but since then the Club has developed along with the increased interest in tandems, extending the range of services and benefits it offers to its members, and currently the Club has a world wide membership of over 6,000 members.
TRANSform Scotland the campaign for sustainable transport for Scotland
Cycle Clubs in the area

Musselburgh Roads CC
Hawick CC
West Lothian Clarion
Kelso Wheeelers
Peebles CC