If you want to actually enjoy the drive, try this: Instead of just taking 80 striaght across the country, follow a more interesting route.
From LA: I-15 through Las Vegas, up through the corner of arizona and through western Utah. Take I-70 East to Denver. I-70 is like 10,000 Times more scenic than I-80 in that part of the country. The speed limit is 75 on both of them. You'll want to do this part of the drive during the day, it'll be the most fun part to watch. My suggestion is to spend the night in LV, and get up and out early the next morning. If you like driving, Denver in 1 day should be fine. You will be driving over vail pass on this route. I doubt you'll need chains this time of year, but it'd be a good idea to have them.
Spend the next night in Denver, then head out 25 North through Wyoming the next day. you want to avoid the plains states as much as possible Kansas is 420 miles of straight, flat, corn fields. I'd take 25 to 94 East, across the northern part of the country. This does kinda take you out of the way, but it may very well be worth it. Stop somewhere along the way in a motel 67, stay the night and visit your friend in MN the next day. After leaving MN, You can head down towards Chicago, and then take 80 east to NYC. This should take you two days.
Total travel time: 1 day to NYC, 1 more to Denver, 2 to MN, and 2 NYC. ^ days, not too bad, but not too fast to miss everything. You don't get a lot of chances to drivbe across the country.
I did the California Coast to Palm County Florida in 4 Days. It was too fast.