There is a shop that sells second hand and new bikes on Scalabrini and Honduras, there is also one on Sarmiento and Bulnes (opposite Plaza Almagro).
I have not bought a bike yet so I offer no testimonials. Good luck.
Cyclists aren't that uncommon in Buenos Aires - which is always a good sign, drivers are used to dealing with bikes on the road and once you work the rules of the game out its actually a great way to get around the city.
There's a tonne of places to go biking in BA -- basically everything on the riverside of Libertador is bike paths. If you're in the Palermo area and want to avoid traffic I'd head along Paraguay or Honduras (I think those are the main two that cros Juan b Justo) and go into P Hollywood, then hang a right on Ravignani or Carranza and you can cross Cabildo over the bridge at Carranza station. from there you can take any of the streets (Dorrego or Ravagnani) down to Campos, and either head straight on Dorrego and cross Libertador then hang a right at the first light and you're at the entrance to Plaza holanda, or go into Las Canitas and cross Libertador with the lights and go into the park at Olleros and do the loop of the golf course.
From the golf course you can head over the bridges into Ciudad universitaria or follow the parks up to Barrancas de Belgrano. From Plaza Holanda you can basically make your way all the way down to the estuary out front of Puerto Madero by going through all of the parks and back streets of Palermo Chico / Barrio Parque. You can also go from Ciudad Universitaria around the back side of Aeroparque and bike the boardwalk that is out front down to the Club de Pescadores.
If you live anywhere near the parks, you can get some nice cycles without having to go into traffic.
If you're looking for guided bike tours Bicicleta Naranja in San Telmo offers them (with or without your own bike) and I think they can also provide maps of their rides -- google them and you'll find their site.
btw -- speaking from very recent experience... if you do the loop from the golf course around the back of Plaza Holanda, take care when you're coming around the turn on the Figueroa Alcorta side! There's a point where the bicisendra gets narrow and on one side there's a metal barrier for the road, and the other the wall of the train bridge overhead... I lost control there yesterday when my chain jammed and stupidly I looked down to see what was happening instead of looking forward and ended up taking a nice gouge out of my shin on the barrier -- in the end had 10 stitches, a tetanus shot, 48 hours of antibiotics, and a 4 hr wait at the guardia... make sure to bring your prepago card with you if you're out on your own, lol!