I recommend laying out your friends' locations (and thus your approximate routes) on a map.
Then seek attractions which lay anywhere near those routes.
Select from natural sights, National Parks and Recreation Areas, downtowns which intrigue you, museums (even if you go to a small, obscure one in a smaller city), a restaurant for lunch if you've seen it on TV.
Swerve off a line of travel to merely hit another state!
If you're out West don't bother going to Wall Drug. It's just a drug store.
Trips like these can become "once-in-a-lifetime" events because we never know what circumstances come our way.
Your time freedom may evaporate.
EVERYONE'S friends grow less able to accept you as an overnight guest to facilitate such a trip. It's inevitable.
I've done trips like this and think back on all of them fondly. My daily mile totals could be 350 to 500 but there have been plenty of 125 milers. On a long road trip a short day is quite restful.
Drive down a coast line and you'll stop to experience the setting, believe me.
The same goes for the High Southwest.
It won't kill you to check into a motel early on a lovely afternoon and write postcards and thank you letters.
Bring a sketch pad and some pencils.
My longest driving day was 861 miles from Wakeeny, KS to somewhere in KY, IIRC. I was in a rush. Kira