You could just say let's go see the Giants play. It's not a question of which stadium they are going to be playing. For American sports, I rarely refer to a stadium by sponsor name. In fact, I prefer to know the irreverant names for them. In Dallas, the cowboys play at Jerry World. When Barry Switzer was coaching, the stadium was referred to as Switzer-land. I also refer to stadiums by their Stadium Formerly Known As like I always used Candlestick instead of whatever corp name stamped on it.
Ah, I see your assumption. I don't listen to announcers ;P
Also, I tend to watch very very little American sports. I'm pretty much a die hard English Football fan, and their stadiums have much more interesting names as well as some fun nicknames. The stadiums with corp names tend to be new money/onwers to the clubs. ManCity's Etihad (Emptyhad) comes to mind. Otherwise, "Stampford" Bridge, Old Trafford, Anfield, Goodison Park, St James' Park, Loftus Road, Stadium of Light, any and all much better than Corp$$OfTheSeason.
I am very conveniently ignoring the corp$$ on the jerseys. It doesn't fit my narrative here =)