Renting is expensive due to the monetary exchange rate. My brother-in-law got on craigslist or something like it and bought 2 used bikes then sold them when we left a month & 1/2 later. The Bike Station has used bikes but its hit or miss on finding a bike that fits you.
We biked the western part of the Hadrian's Wall. We loved it. The Union Canal starts right in downtown Edinburgh and goes out to the Falkirk Wheel.