Can I give the qurbani money to charity instead?

Why the animal itself matters

Qurbani is not only about feeding people. It's a ritual linked to the story of Ibrahim and his son, done at a fixed time, with a specific animal, in Allah's name. The Prophet ﷺ sacrificed every year and encouraged those who could afford it to do the same; he even said that someone with the means who doesn't sacrifice should not come near the Eid prayer place (Sunan Ibn Majah 3123). Scholars say this shows the act of sacrifice is what's asked for, not just its price.

The Quran explains what really reaches Allah:

What the schools say

• Hanafi: qurbani is wajib (required) for an adult Muslim who has the nisab amount during Eid. If the days pass and someone failed to do it, they should give the value of a sheep in charity as a make-up. That's a late repair, not a free choice.
• Maliki, Shafi'i and Hanbali: qurbani is a strongly recommended sunnah. Doing it is better than giving its price as sadaqah, because it follows the Prophet's ﷺ practice.

So under every view, if you can afford it, sacrifice the animal. See What is qurbani and do I have to do it?

Qurbani is already charity

The meat is meant to be eaten and shared, and much of it goes to the poor. In one year of hardship the Prophet ﷺ even told people not to store their qurbani meat beyond three days, so it would reach those who needed it (Sahih al-Bukhari 5569). If your heart is with people in crisis, the easiest answer is to book your qurbani through a trusted charity working in a poor country. See Can I pay for qurbani abroad instead of locally?

What if I can't afford it?

If you don't have the means, qurbani isn't asked of you, and giving whatever you can as sadaqah is still rewarded. Also keep in mind that zakat, sadaqah and qurbani are three separate things; one doesn't cover another. See What is the difference between zakat and sadaqah?