Advice for tourists with a 12 month old?

Hello! We’re a family of 3 (my baby, husband and I) from East Asia and traveling next week to LA. We have a tour guide and coaster booked for the main sightseeing spots (Griffith Observatory, Beverly Hills, Santa Monica Pier, etc) but we have around a week to just go around the city and explore on our own. Some activities we’d like to do are taking dance classes at a studio in Melrose Avenue and doing shopping at outlets. We’re planning to purchase a car seat once we land as well, and will be staying at Intercontinental.

Would we be better off renting a car where we can just install and leave the car seat? Or if we’re exploring a lot, would it be better to just Uber around and bring the car seat around, like in a backpack bag? Any advice is appreciated!