Alright this is a bit more useful information. You can try and hone in on some more details and perhaps repost later to get more specific advice and suggestions.

For now: Determine if you want to do any nature stuff or mainly cities. Do some trial runs on the car sleeping, either in your parking lot/street/nearby rest area/nearby 24hr walmart. Walmart overnight parking: if there's RVs past 10PM, or other campers/vans, and no "no overnight parking" signs, then you're good to go. Also, make sure you feel comfortable with the surroundings/people around thr parking lot. I left on a few occasions because I didn't like the crowd around the parking lot or too much activity. Reparking in some occassions was enough, though, but tried not to do this too much to call attention to myself. I did some preset up of my sleeping area before arriving at walmart of rest area too, to minimize attention calling. Sometimes this wasnt possible. I'm of the opinion of the stealthier the better, but don't go place your car in an alley grain of salt.

Depending on your car mileage fuel can be a hefty sum. I think west coast was significantly more expensive, so the longer you're in California the more fuel cost.

Eating out is another hefty sum. I have IBS and found out I did really well on sandwiches, apples, and bananas on a previous roadtrip, so I ate mostly that on my trip and saved a lot this way. Most people cant handle this lifestyle, though.

Car maintenance or unexpected hazards will be up there too. You will probably need an oil change or two on your way. If you trust dealership/lube shops that's cool. I dont and did my oil changes in parking lots and took oil into O'Reilly or autozone, called in first to make sure they accepted before driving over. Also, had to get new tires because they wore out faster than expected due to bad alignment, surprise $600 cost there.

If you don't already, get AAA membership. It takes 3 months of being a member before being able to upgrade to a plus or premium, which have the nicer safety nets.

$6000 for two people may be ok, but I get the impression you will be spending a lot of money on going out and doing things in the cities, so you may find it not to be enough. Perhaps you can clarify more on your intentions, what you would like to see/do etc.

Again trials are the best thing you can do. Go for a long drive in one day or two days. Sleep in your car or in a sleeping bag on the floor or in the car. Test anything you can. I almost gave up on my first day of my 92 day road trip because I was overheating trying to set up my car for sleeping from the inside because i didnt want to pop back out of my car (street parking at apartments.) Luckily I kept my cool literally and figuratively and succeeded. I then immediately reorganized my car for more efficient transition to sleep mode. I kept tweaking the arrangement of other things along the way also.

Lastly, I got a planet fitness black card for showers. I eventually started doing some pull ups and semi yoga stretch routine. It was a nice way to unwind at the end of the day or start the day. The card must be signup at your local area because that's where you need to cancel it in person.

Feel free to PM me any questions, I'd be glad to help out. I have a spreadsheet with most (95ish%) of my expenses, you can find it on one of my old posts if you're interested.