you can do the cost yourself -- Google uber price estimate . Self help is such cases is the best help.
It all depends on what you plan to do in Monterey -- You can rent a car and walk around and see things and it will be easier to go to Carmel and Pacific Grove and the portions of the Big Sur which you want to see with a car
Now where is this car seat in the Uber coming from. Uber does not have car seats and it would be ridiculous to haul a car seat with you and take it off in every uber you sit in.
Please think this through. This is apples and oranges
Uber does not provide car seats in California.
So rent a car with a car seat or bring your own.
If you're absolutely against renting a car with a car seat, then look into the bus options. You can either take MST #86 from the airport to Salinas (https://mst.org/wp-content/media/86.pdf), then another public bus (probably #20) into Monterey. Or you can take the free airport shuttle to the Santa Clara Caltrain station, the Caltrain to Diordon, and the #55 into Monterey (though I've done this and it's very, very time-consuming). This all depends on whether or not the bus schedule times work with your plane's arrival.
Another option is the Monterey Airbus, which does provide the required child safety seat when requested in advance: www.montereyairbus.com/child-safety-seats. But it will be very expensive for multiple people.
Bottom line: it's cheaper and easier to rent a car and bring your own car seat. This is what we do when we travel. Even if you do request a car seat with your rental car, it's not a guarantee that you'll actually get one. And they're very expensive to rent.
We'e been out of the car seat business so I defer to others re availability -- We did not have problems last decade with availability of car seats -- and we only go with Hertz or Avis
As far as price goes
Free use of one child, infant or booster seat
AAA Members receive the FREE use of one child, infant or booster seat with every rental, a savings of $13.99 per day! In addition to the savings, additional benefits of this special offer are safety, security and convenience. Members can enjoy the safety and security of knowing the Hertz seats are properly cleaned and maintained. The convenience of using a Hertz child safety seat versus dragging a personal seat along on vacation is a primary consideration. Advance reservations are required and safety seats are subject to availability.
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