Hi, Hayley
Welcome to the Forum. It looks like you're new to Trip Advisor. I'm going to recommend that you edit your profile and include your city of residence so that it displays beneath your screen name as it does for most of us. Knowing this info will help us to help you better. Yes. you can simply tell us in your response but this info will be important for most postings that you submit to Trip Advisor so putting it in the profile will save you the hassle of saying: "Coming from XXX" every time you post.
To your questions...
1. I'm wondering why you aren't arriving at one airport, like LAX and returning from another, like San Diego. This will save you the drive from SD back to L.A. to drop the car. (This is when knowing where you live comes in handy because if you live overseas, for example, flights out of San Diego aren't that great).
BTW, it's helpful if you can be as specific as possible. So, for example, what time of day are you departing LAX? Saying 'in the morning' isn't very specific, especially when we don't know if the flight you're taking is international or domestic.
I mention the above because 'staying near the airport' in L.A. is awful so if I can suggest another place (not too far away), I'll do that but having details about your flight will be helpful in that regard.
I am not trying to be difficult when I say that you needn't say "No Disneyland" because Disneyland isn't in the City of L.A. (where you submitted this posting); it's not even in the same county as Los Angeles.
Again, saying medium-sized budget is hard to work with because if you're from a place where things are cheap then a hotel costing $200/night will seem expensive.
AirBnb better known as 'vacation rentals' or 'holiday rentals' are seriously restricted in the greater L.A. metro area. Cities like Santa Monica (the beach) and West Hollywood (the Sunset Strip) don't allow these unless the property owner is living on the property.
If your only reason for booking these is for 'ease of parking' (although, tbh, I'm not sure what that means), book a hotel. All hotels have parking facilities. As far as a private washer/dryer, that's less common but there are hotels that offer this feature. (Some hotels are former apartment buildings that offer rooms with separate bedrooms, kitchens, etc as well as laundry equipment).
Bottom line: be careful booking holiday rentals in L.A. as some are not legal. Check with us first before you book.
We don't really have a city center, here. L.A. is a merging together of lots of cities, towns and hamlets so there are lots of city centers and the city is very spread out. Where you stay should be based on your itinerary, your budget and other factors).
I just noticed that you, like others, are pronoun-phobic. Please tell us whether you're traveling alone or with another(s). Kids? Ages? This will affect where you stay (number of beds, suitable neighborhood, etc).
Re: your current plans:
"- Day 1: 2:00pm Arrive at LAX...pick up rental. Check in AirBnB. Explore Central LA...typical Walk of Fame, Chinese Theatre, Market, Rodeo Drive."
Again, we're not sure when you're actually getting into the car if you're landing at 2 pm. If this is an international flight, it will take a while to pass through the airport. The car rental lots are all off-site so upon emerging from the terminal, you'll then have to wait for the shuttle for the car rental company of your choosing.
You could be in the car at 3:30 or 4:00 or ?
And, you haven't mentioned 'travel dates' so are you arriving on a weekday or weekend? If the former, you'll be driving during afternoon 'rush hour' which lasts until about 7:30 pm. As such, even though your itinerary isn't very large on this day, you may not be able to do all of it -- especially if you're heading to an accommodation that isn't in any of these areas.
Your plan on day #1 is to visit the Hollywood district of L.A., the Beverly Grove district of L.A. and the city of Beverly Hills. These aren't terribly far apart from one another (20 minutes ordinarily without traffic) but at each site, you'll need to park which will eat up some time (let alone the time it will take to retrieve the car and the time it takes to walk between the parking facility and the attractions).
"- Day 2: Griffiths Observatory, The Getty, Getty Villa, Universal Studios CityWalk (free area)"
This is also a fair amount of driving. Are you saying that you plan to visit the Getty Center and the Getty Villa on the same day plus Griffith (<-- note spelling) Observatory and Citywalk. All of these have horrible parking facilities and, again, they're not near to one another.
For the Observatory, you need to park on the road leading up to the Observatory and then trek up the hill to the attraction (and back). The road is subject to traffic and it can be time-consuming finding a parking space (you could drive up the hill and find NO PARKING when you arrive at the top; then you'll need to head DOWN the hill, looking for a space). All of this will take time (let alone walking between the car and the attraction).
The Getty Center's parking is at the foot of a hill on the top of which is the galleries. You must line up and ride the funicular to the top (30 minutes during busy times; 15 minutes heading down the hill). This is in addition to the lines entering the parking facilities.
The Getty Villa always has a line as you enter. You have to stop at a booth halfway up the hill to check in and there are always cars in front of you. Then, you drive up to the parking facility, hunt for parking and then there is a bit of a trek up to the building itself.
Similar situation with City Walk. I have no clue why you want to visit this. It's a shopping mall with chain restaurants that you can find all over the city. Plus, you have to pay for parking (and endure the lines entering and exiting the parking facilities). Drop this!
"- Day 3: Drive to Santa Barbara for Day/Evening trip, return to LA at night"
I don't have a problem with you doing this if you want but start early and be prepared to be stuck in traffic on the way back.
"- Day 4: Walk Venice Beach, and Santa Monica, Beverly Hills, Little Tokyo"
Have you looked at a map? The beaches are at the WESTERN edge of the metro area; Beverly Hills is in the center (and didn't you visit it on day #1) and Little Tokyo is in downtown L.A. which is near the EASTERN end of the city. So far, the most memorable part of this visit is the driving!
I'll let others comment about San Diego.
"- Day 7: ???? Currently a free day. Suggestions welcomed. Shop/eat?"
If you stay overnight in Santa Barbara, you can stop at the camarillo premium outlets on the way back and then head to the coast and eat in Malibu on the way back to L.A.