A few things...
I don't recommend walking around the strip (Cumberland Ave.) with open alcohol. Although I have seen many do it and have done so myself, the wife and I were once with another couple who had beer in URC's (ubiquitous red cups). They were very surprised to be ticketed for open container. So, even though it doesn't happen often, it does happen. As has been said, you won't have any problems at tailgates. If you must, a good strategy would be to put it in fast food cups with lids.
As has been said, getting there early is must. I recommend going to the downstairs bookstore in the Carolyn Brown University Center. It is THE best shop for Vol stuff and attire. Two blocks from the stadium.
Check the gameday page on utsports.com for details on the Vol Walk and the band marching to the stadium.
There are excellent tailgates in the parking lot across from gate 21. Most everyone will welcome you with open arms. But, for courtesy, I recommend taking your own libations and maybe something for the host.
Best of luck and GO VOLS!