If you go to the North Rim of the Grand Canyon you can visit Zion National Park en route. Yes, from LA go north on Highway 1 to Monterey and then head over to Yosemite. It's one of the most scenic roads in America. New Orleans is one of the more interesting cities in the U.S. but it will be extremely hot and muggy then with the possibility of a hurricane.

If you can find the time, the drive up Highway 1 through Big Sur is one of the best the US has as far as drives go.
OP, in the route I provide above, this would be the section between SLO and Monterey.
I would pull 3 days from the lake placid, ithaca area and go to NOLA.
OP, the underlying question here is whether you want to spend more time partying or more time outdoors.
Though if you were to take something out, I'd say Ithaca and Niagara. Keep the Adirondacks (if you consider them).

If you go to the North Rim of the Grand Canyon you can visit Zion National Park en route. Yes, from LA go north on Highway 1 to Monterey and then head over to Yosemite. It's one of the most scenic roads in America. New Orleans is one of the more interesting cities in the U.S. but it will be extremely hot and muggy then with the possibility of a hurricane.
Hurricane thing is ridiculous

Another option for you. Do your homework on the Niagara thing, doesn't seem like a fun place for a single dude, could be wrong?
8 Jul - NYC
9 Jul - NYC
10 Jul - NYC
11 Jul - NYC
12 Jul - SF
13 Jul - Yosemite
14 Jul - Yosemite
15 Jul - Lee Vining or Tom's Place
16 Jul - Las Vegas via Death Valley
17 Jul - Zion
18 Jul - Zion
19 Jul - Grand Canyon
20 Jul - Grand Canyon
21 Jul - Las Vegas
22 Jul - LA
23 Jul - LA
24 Jul - Coast Drive
25 Jul - Coast Drive
26 Jul - SF
27 Jul - SF
28 Jul - SF
29 Jul - NYC
30 Jul - NYC, leave
Might consider getting a www.escapecampervans.com
in SF and camp in Yosemite, Eastern Sierra's, Zion and Grand Canyon, easier to get a camp spot and more fun to stay in the park. Turn the van in at Vegas and get a car for the LA-coast part.
Started you in the west in SF so you can hit Yosemite mid week.
RE: Yosemite. In summer it can be very crowded, more so on the weekends. When things get really bad, they even close the park entrances.
I will repeat: lodging inside Yosemite Park, including most campsites, books up months in advance. It may be impossible to find a place to stay within the park now, except for some of the more remote campsites. You should look into booking NOW. Keep trying--sometimes there are cancellations.
I think the point being made is the very low risk of hurricane activity on any specific date in July ... you're probably more likely to get mangled in a taxi driving in from the airport.
... and go to NOLA. there is nothing cooler than walking up Bourbon st with a cup o Joe at dawn.
I don't have any strong feelings about New Orleans one way or the other, but walking up Bourbon Street with all the other badly dressed, rather lubricated rubbernecks is just the sort of touristy image of the place that keeps me away (in addition to bad honky-tonk jazz of course).

Hurricane thing is ridiculous
How do you spell KATRINA?
you spelled it correctly but a hurricane is still an irrelevant concern.
The odds of a given vacation intersecting a proper hurricane are quite low, and 95% of the time, a hurricane watch is no big deal. The only concession I'd make for that time of year is to not book prepaid accommodation in the rare case it's a good idea to zig instead of zag for that part of the trip.
I will however note that July is rainy season along the northern Gulf coast, and some of our ordinary stalled front rain systems can generate 15-30 cm of rain in 24 hours, and are pretty indistinguishable from many a named tropical storm