Try Bicycle Sport Shop, they have a great rental fleet, www.bicyclesportshop.com. They have a north store and could transfer a rental up. I live north but west of Round Rock, no real trails unless you are looking for mountain biking then Walnut Creek Metropolitan Park is pretty fun one. Not crazy technical, just fast and flowy.
Road routes, Round Rock is kind of boring in my opinion so I don't ride over there. East of 35 is mostly flat and not my thing, plus I am mostly a mountain biker. If you really want to do some riding you could join Austin Cycling Association and have access to a ton of maps, https://www.austincycling.org/civicr...t?reset=1&id=4. Depending on where in Round Rock they are you might be able to get advice from any of the shops located on Parmer Lane in Cedar Park (just west of RR). BSS has a location and there is also an AJ's Cyclery.