OK...I see where that is. I've always started my Parmer rides just to the west of Mopac, but looking at Google Streetview, it looks like there's a nice wide bike/breakdown lane all the way to Lamar...so yeah...Parmer looks like a great choice for you if you don't want to drive your bike to another start location.
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2014 Specialized Roubaix2003 Interloc Impala2007 ParkPre Image C6 (RIP)