Yes, the place just outside Calangute market is the place to go to hire bicycles, and is cheap. If you are going to be here long term and want to buy one, you have to go to Panjim or Mapusa. Prices start at around Rs 2,500.
I am a long term cyclist in Goa. They're a great way to get around the main Candolim/Calangute/Baga area, especially on the back roads,as they're all flat. Also good for riding around the quieter roads to and from Anjuna (flat) or Vagator (hilly). Even better if you can make it as far as Morjim and Mandrem, though there is a steep hill in Siolim which you will have to walk up (most bicycles here don't have gears).
During the day, watch out for pedestrians as much as for cars and buses - the only time i have ever been knocked off it was by someone crossing the road without looking to see what was coming. At night it's a different matter, and you need to be very careful. Rented bicycles don't come with lights, though you can buy these in the cycle shops in Mapusa and Panjim. The roads are pretty busy and dangerous around the 7 to 8 pm "rush hour", though they're quieter again after around 9. Early mornings are best - cooler, more peaceful, less traffic.
I just wish that more poeple cycled, and less people hired scooters. And, with taxis charging so much these days, it saves you plenty of money as well as keeping you fit.
Good luck.
Phil