How should an educational institute woo good faculty?
Money

First, there's very little way - I think - for a university to improve its standing across the board. Institutional reputation on the level of say, an Ivy League school, where everyone assumes each department must be excellent because they're at Ivy is a tall order, and one that I suspect is impossible.

But in a particular field (or a particular School)? Money. And the willingness to take risks. A few ways to help:


Find a few key faculty members. Established researchers with very solid reputations, and see if you can poach them. This might not just be a question of "how big of a check do we need to write"? There are other factors. A considerable bump in prestige. Quality of living perks. The chance to shape a promising new department in ways that you rarely get in established departments - a chance to be the formative voice in something.
Be looking for promising potential new hires. Maybe they're coming out of the universities you hired these key faculty members from. Maybe they're coming from top schools generally. A generous start-up package, extra lab space and internal funding, a generous tenure process - these are things that might lure top candidates away from a harder path at a more prestigious institution. It represents a risk for both parties - you might get a dud researcher with a good degree, and they might get a department languishing in obscurity. But if it works, it works very well for both.
Buy something big. Are there no Expensive Piece of Equipment equipped centers in the region? Become the people who have one.