Unless there's a NASA facility nearby, your best bets are either a ham repeater that rebroadcasts the audio (one of the rare times this activity is actually permitted, by the way) or hearing directly on HF. Grove's NASA page is linked here, along with a couple of others - just select the 'Frequencies' topic, then scroll down to the NASA section...
There are multiple freq lists on the web for shuttle monitoring. HF is a good place to look for activity, 10.780 USB is a good start on HF for support comms. You can try the primary UHF air to ground freq (259.7) for takeoff. I've heard direct shuttle comms on this freq before from Charlotte. I think they were blasting off along the east coast south to north.