If I'm willing to buy a piano for $1000, how for should I be willing to drive to get one?

How far*

Far enough to get a good deal on one that's worth having and not in need of a lot of repairs.

Do you have a truck and a few strong friends riding along with you or are you paying a shipping company to move it?

Depends on value of your investment. If it is a $1000 piano, not far. If it is a $5000 piano lots farther. Craigslist has loads of them for $100 up, some free for the taking.

No further than you will go to examine it first. A cracked soundboard makes it worthless. Bring your truck, helpers, money, and meet a piano expert there and pay him or her.
Oh, and pianos need special dollies that won't dig grooves into floors.
All in all, I would go see one, hire an expert, plus hire a piano mover. Costly.

How far should you be willing to drive? Well, it all depends on you and what you're willing to do.

I may be willing to drive for hours to get a good deal on a good piano, but you may not be willing. Asking us what you're willing to do, is not a question we can answer, because we have no idea what you're willing to do.

So, what are you willing to do? Only you can answer this question.

A 1000 dollar piano is not very good, normally, if you find a great one for 1000 drive 100's of miles. I drove about 300 miles to get a very nice free one, once.

I will assume you have a truck, and 4 or more men to help move one. They are heavy.

Also you understand that after you move a piano, it must be re-tuned