Good question, and one that's been plaguing urban parents for a generation or so.
The short answer is no, your grandbaby doesn't need a car seat in a taxi. Car seats are not required for commercial vehicles -- buses, taxis, limos, trolleys, etc. Of course, if you have a car seat with you, cab drivers are more than happy to put it in the car for you.
But that's the problem: schlepping around a bulky baby seat everywhere you go, just so you can strap the baby into it for the cab ride. Some strollers have car-seat attachments, so you could do double duty with one of them. And then there are Babybjorn frontpack carriers; strap yourself and the baby in with the seat belt. Failing that, there's the most typical solution: Strap yourself in, hold the baby, and pray. It's not the safest way to go, but at least in taxis, it's legal.
Note that there's no more trolley. The Strip Trolley has gone out of business. Dozens of Deuce double-decker buses now ply the Strip, the only public transportation on the Boulevard itself (the monorail runs parallel).
