I don't buy the lower travel time thing, not unless your trains or whatever are running every five minutes. In practice public transit has always at least doubled my travel time. Waiting at stops (a) introduces substantial latency that (b) is unpredictable, forcing me to pad my travel times further. I mainly use it to avoid parking at the destination.
DC and LA are both infamous for having bad public transit systems, so don't base all your decisions on your experience there. Within the USA, Chicago is really good - taking the L is way faster than cars because you get to skip road traffic and the trains come very frequently. I've heard mixed things about NYC (some very positive, some very negative, likely depending on where you're traveling from/to), but have no experience there myself. Outside of the USA, there are lots of countries with fantastic train systems (e.g. Hong Kong) that are way better than driving.
Besides NYC that's been my experience as well -- US cities are designed for driving as the primary transportation method. Even mass transit in the US is often pitched as something to make life easier for drivers by lowering traffic.
Lots of places talk about the importance of walkability and mass transit but if you actually look at most transportation budgets the vast majority goes to automobile infrastructure. Even what passes for "pedestrian infrastructure" in many places is there for the benefit of drivers[1]. I mean, it makes sense because everyone in the US drives everywhere, but it's a chicken-and-egg problem.
Mostly DC metro rail and a bit of LA buses, FWIW.