Jack and Adams has a group ride that leaves their shop every Sunday morning, wheels down 8:30am. Three levels, beginner, intermediate, and advanced. Based on your preference I would say your in the advanced group. They don't wait for dropped riders in that group, so if your having an off day you should be familiar with the route before hand.
Lots of bikers (no real organized group ride usually though) ride Ronald Regan Parkway (aka Parmer) out to Andice and bike. Fairly easy ride, some light rollers, and usually some wind to contend with, but nice wide, fairly clean shoulders. Start from Avery Ranch and it's about 50 there and back.
Loop 360 from the Aboretum to South Mopac and back is +/- 26 miles. That ride lets you add just the right amount of pain since you have the chance to dance with any one or all of the 7 sisters of pain.
3. City Park
4. Bell Mountain
5. Lost Creek
6. Courtyard (one of my personal favorites)
7. Spicewood Springs road and Adirondak
I might be missing some, but those are the ones that stand out to me.
The dam loop is a pretty good ride. Austin Tri Cyclist has a group ride that leaves from their shop on Saturday mornings I think its wheels down around 8am, not sure.
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