Which motorcycle is best for me?

I was looking at bikes like the Honda VFR 800 or the Triumph Sprint ST but I want to know what you guys think. My dad goes on yearly bike trips and they do about 500 miles a day and I would like to go with him without having to quit after one day because I'm too sore. However, I want something with some speed, good handling and a sporty feel. I have a lot of experience riding and I'm comfortable with bikes over 1000cc. I ride a 1983 GL1100 right now but I'm looking for an upgrade.

The bike will not be the problem, the rider will need to cope with the distance, you will need to build up to the distance by taking trips over shorter distances. Either of your choices seem reasonable.

I'm an experienced motorcycle toured so advise you from that experience.
Firstly whilst 500 miles may seem a lot in fact it depends on what roads this is done on as that will determine the time spent in the saddle. If there's a good proportion of fast mainly straight roads, although potentially boring, if will be quicker than 500 across country roads.
Another consideration is the need to carry luggage which some bikes are better at than others.
Unfortunately there's no way to see where you live so some of my suggestions may not be available. Also you have not said used or new?

Triumph Sprint - not the one with the under seat exhaust as it cooks bottoms but otherwise if you find it comfortable then its a good choice.
VFR - not a terrible choice but not great if you are tall.
Honda Pan European - a mile muncher with a well proven and reliable design and good value to run. Great pillion accommodation.
Yamaha FJR1300 - very capable and fast. UK Police now use this a lot for motorcycle training.
Kawasaki GTR 1400 - a bit hard on tyres and handling suspect.
Suzuki 1250 Bandit or similar. Mega value and fully faired good for touring.

Whatever you choose you may still need to make modifications, most tourers do, like seat, heated grips, higher screen etc.

If you only go on this trip once a year, then I would go for the ST. You still got 50 other weeks to ride and the ST is the best choice. Most are too big and heavy for daily use.
And the Triumph looks nicer too.

Neither of those bikes would be suitable for 500 mile per day trips.

I may also add that I would commute to work and school, which is about 30 miles of highway riding so most of the miles I put on the bike would be from interstate. Also, I've looked at those bigger sport tourers like the Pan European and FJR. They seem great, but a bit on the large side, as I ride a large bike now I'm looking for something a bit smaller.

Go for the VFR800. It consistently wins best touring bike in a shoot out for a reason… And the reason is it's so damn good.
You can find out more my watching a group test on Men an Motors on YouTube and see the pros and cons of ownership of Honda's sports touring flagship.