Do any houses in the westerlands(current houses, excluding cadet Lannister houses) have a substantial amount of gold from mining like the Lannisters- maybe the paynes?

I would say that the norm is that Houses with their holdfasts in the hills (as opposed to say Crakehall or Cornfield) have a good deal of income from mining precious metals (mostly gold, but not entirely, hence House Serrett’s seat being named Silverhill), unless otherwise indicated. (”The Westerling mines had failed years ago.”)