She buys whatever she wants without sparing any expense.

Literal

She [topic-は] money [on-に] thread-eye [object-を] not-attaching, wanted thing [object-を] buys.

金に糸目をつけない is a beautifully concrete idiom — 糸目 ('thread eye') is the small hole in a kite frame through which the kite-string passes, the point that controls how high or low the kite flies. Without a 糸目 limiting the string, the kite flies free with no restraint — and metaphorically, money 'flies free' without any limit. The literal meaning ('not attaching the thread-eye on money') translates to 'spare no expense.' The negative form ~ずに ('without doing X') is the bookish/written counterpart to ~ないで, here giving the sentence a slight literary feel.