I sat at the table next to TR, so I assume most of the interaction would be the same for you. Here's just some random stuff I remember:
1.) Lucas Steele comes out and gives you pierogi during the preshow, and gives the little spiel about how you're seated in a high traffic area.
2.) You generally just make mountains of eye-contact with performers, and lines are often directed towards you during solo songs (like in Dust and Ashes and No One Else).
3.) During Natasha and the Bolkonskys, Natasha and Mary sit between tables TR and TQ and sing some of their number there. Be attentive when this happens: they'll probably ask you to scoot over!
4.) During Letters, you'll either get a note from Hélène, Sonya, or Josh Canfield (or, if he's out, a swing). There's a stool next to TR that they all sit at during that number. I got one from Sonya.
5.) During the rave bit in The Duel, two ensemble members did "cocaine" at my table.
6.) You get an egg shaker during Balaga, and the actor playing Balaga gave me a high five.
7.) From Pierre and Anatole on, Hélène sits at the aforementioned stool and just sobs until the end of the show. It's insane. Amber Gray is insane. Life is wild.
8.) Nick Choksi has a habit of remembering onstage audience members, so if you stage door he'll probably make a comment if he recognizes you.