I often visit old churches and play my guitar in their gardens or near their outdoor Rosary walks or Stations of the Cross, where available. I do NOT participate in NO services, but my home parish is a GORGEOUS church, built in 1903, that still has its traditional altar (which, by the way, is still referred to as an altar and treated as such, although there are no traditional Masses said there anymore). I visit there whenever the doors are open, because it's stunning and it was my dear maternal grandparents' home church (may their souls and the souls of all the faithful departed, through the mercy of God, rest in peace).
I generally don't go into strictly NO churches unless there is some unavoidable reason (like a wedding or whatever, but I have never taken part in one and never will), or churches where the traditional altar is gone. If I do go into a church that has a picnic table in front of the altar, as others have said, I respect the presence of the saints' relics in the altar and the presence of the Tabernacle where Our Lord WAS kept sacramentally.
Besides, Novus buildings are almost all UGLY, UGLY places. All hippied-out with their flannel banners and exposed wood beams and acrylic (not glass) windows. Just nasty. Yecch. I was at a chapel the other day that was built in the early 1900s and has been totally NO-centric since VAT 2, but I stayed outside unless I was in the gift shop, where the old ladies still sell medals and other items you just can't find in stores anymore. The chair that the NO presider sits in during their service looks like a prop from a Flintstones cartoon... looks like chiseled rock or something... almost a joke if you consider what they SAY it's for... Mass? looks more like something a caveman would sit in. Anyway...
My best advice is to behave like you're in a traditional Catholic church or chapel when you ARE in one, Novus Ordo presence or not, and avoid strictly NO buildings or churches where they have stripped the church of its altar.
By the way, that brings up another question... what happens to the STATUS of a church when the Altar, with its relics, which was consecrated validly, is taken out of a church? Does that deconsecrate the church? I know that NO tables have relics in them, too, but is the rite of consecration of a NO table the same as the rite for an altar?
Our Lady of Lourdes, pray for us.
Sacred Heart of Jesus, have mercy on us.