
Cosco Kids
Scenera Next DLX Convertible Car Seat
Super light, cheap, great for air travel, but outgrown fast.

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My opinion is the less luggage to deal with the better. That said, the rental car seat is silly cheap and bare bones quality. It works if you're in a pinch or not expecting to use it much, hit or miss on cleaniness. I think Avis mostly uses Evenflo Tributes. You can also rent car seats online and they deliver to you with much better quality and prices. They don't install the car seat for you most of the time, and I would just install it myself for peace of mind that it's installed correctly (you should really know how to do this regardless). For getting to the airport, what we've done is get a rental car with a car seat, and just use that the day of to get to the airport, especially if the airport is in another city.
When we for with our 20 month old we used the Evenflo Tribute LX. She was right at the edge of there weight limit, and maybe a lb or two over fully clothed and stuffed with food. But it worked really well for us. It’s only 9.3 lb so relatively lightweight. My husband was able to use a heavy duty caribeaner and hook it upside down over his backpack so our hands were free. We tried the either Cosco Scenera or Maxi Cosi Romi (I can’t remember which, but they’re basically the same car seat, made by the same megacorporation but under different brand names and Maxi Cosi has nicer fabrics) because it was lightweight and highly recommended for travel. She was right at the weight limit for it (40 lbs), too, but we weren’t able to use it because the straps were comedically too short. Like I don’t think they made it even halfway around her body. That might not be an issue for you, if yours is tall but not wide. Mine was super off the charts heavy and not particularly tall. All to say check the height restrictions, and make sure you buy far enough in advance that you can return it and buy another if you need to. Or plan to buy two and return one. Because you don’t want to buy too far in advance and then they outgrow it by the time the flight comes around. Now that she’s older (3) we like the Graco Tranzitions 3-in-1 for travel. It’s also lightweight. But it’s forward facing only, so not really suitable for a 1 year old.
If you need a small travel car seat, try the Evenflo Tribute or the Graco SnugRide. They're light and easy to set up, plus they should work for your height and weight. If you want more opinions or comparisons, check out borncritic... they have some good guides that might help you figure out those Safety First seats too.
Definitely have been there and it was the same for me — FAs were generally not familiar with how to solve this problem. I don’t blame them one bit either. So many car seats and plane seats out there. We were flying a lot for a good stretch so I ended up buying an inexpensive lightweight car seat specifically for flights that would give me the least number of headaches. Just looked it up and it was the Evenflo Tribute. On Amazon open box a few years ago it was usually $40-50 though I cannot say if that is still available these days. Looks like I ended up buying it on three separate occasions!
Subway is easy for sure but you can get car services or Ubers with car seats or buy a super light travel car seat. Cosco scenara is popular or Evenflo tribute I think. Both are 8 lbs or less and can rear face.
Arecibo car service has them. Haven’t done uber, we have a car and our youngest still fits the doona. We have a ride safer for our 3 year old that’s a total game changer for car travel but had no problem with the Evenflo before we got that. Drivers were usually patient while we installed. Typically the only time we’d be in a car is to/from the airport so we would need the car seat regardless.
I have a rotating one in my girl and a regular one in my husbands. We both prefer the rotating one!

Cosco Kids
Scenera Next DLX Convertible Car Seat
Super light, cheap, great for air travel, but outgrown fast.

Cosco Kids
Scenera Next Convertible Car Seat
Portable, affordable, quickly outgrown, airplane buckle discomfort.

Joie
Mint Latch
Easy baseless LATCH install, lightweight, but quickly outgrown.

Nuna
PIPA Series
High-end travel, easy baseless install, but very pricey.

WAYB
Pico™ Portable Car Seat
Ultra-light, compact travel, quick install, but expensive and outgrown fast.

Ranked #1
Cosco Kids - Scenera Next DLX Convertible Car Seat

Ranked #1
Cosco Kids - Scenera Next Convertible Car Seat

Ranked #1
Cosco Kids - Scenera Next DLX Convertible Car Seat

Ranked #1
Doona - Doona Series

Ranked #1
Cosco Kids - Scenera Next Convertible Car Seat

Ranked #1
Nuna - PIPA Series