I'm a big fan of Sellwood Cycle. They don't have space for you to rent, but they are very straight forward and give great service. It's a small shop that sells a few new bikes (Kona's) and a lot of road/cyclocross bikes on consignment. I bought a used road bike from them and ever since they remember my name and bike everytime I go into their shop.
The owner of the shop is a professional (or maybe semi-professional...) cyclocross racer who is very connected to the local biking scene.
I also have experience with Veloce Cycles. Dimitry fitted me and did a great job. His store has a good vibe.
Welcome to Portland! Best cycling city in the U.S. (if you don't mind the rain).