Will my 2001 Honda Accord be okay driving long distance (800 miles each way)?

I'm moving away about 800 miles for school. I have a 2001 Honda Accord, and my dad says he doesn't think it'll make it because it has 120k miles on it. I'm getting brand new tires for it TODAY, and decent ones, too. There are no brake problems, or any problems at all. He just says it has way too many miles on it to drive that far. I've known people who've had twice as many miles on their cars and were perfectly fine. I don't see the problem.

When I go get my new tires today, I plan on asking them about my trip. What should I ask them, in particular, that could be changed/fixed up? I honestly don't see any problem with it. I might get an oil change, but I don't have all that much money to get everything fixed. What is most important that I get looked at to confirm it's fine to drive?

Also, the 120k miles were just commuter miles. It was never driven in rough environments or anything- just nice, smooth roads. Regular maintenance. It was handed down from my dad who took great care of it.

Added (1). Oh, and it'll be each way because I'm going to visit and look at apartments in a few weeks before I move.

A hundred and twenty thousand used to be a lot of miles on the older cars. However, I have quite a few friends with over 200 thousand miles on their later model cars, It all depends on the maintence records, if it was well cared for you should not have any problems.

Is it a petrol or Diesel engine?

If it's a diesel those miles are no issue, however even Honda petrol engines are fairly bullet proof (the s2000 has never had a blown up engine which Honda love to point out)

Make sure you have decent breakdown cover, get some decent music and enjoy munching up those miles

If it has been regularly serviced and you haven't noticed any fluid leaks then it should be fine if you stop every 3 or 4 hours or so.
Have the garage check the belts and hoses and maybe also lubricate the brake calipers so they don't get stuck part way and overheat (important if there are mountain grades to climb up and over on your trip). It will also benefit from a new air filter and fuel filter as appropriate.

It will be fine

You'll be fine. My 2000 has over 140k miles and I drive it to the bay area from Washington every other year or so. No problems.