It was in fact named after the car company (and not the other way round).
Toyota is rather difficult to reach by public transport. Despite being close to the Tokaido-Shinkansen, it has no Shinkansen station, and it does not even have direct connections to nearby Shinkansen stations. The closest Shinkansen stations are Toyohashi, Mikawa-Anjo and Nagoya, with Nagoya having the fastest connections to Tokyo, Kyoto and Osaka. Toyota's main train station is called Toyota-shi, and approximately one hour from any of the Shinkansen stations, requiring changing trains at least once.
Toyota is, untypical for Japan, a car city with a very good road network and very sparse public transportation.
There is a really nice bridge that looks like it is constructed out of dinosaur bones. It makes for some interesting pictures and a nice stroll in the afternoon.
Rickey's (on the 1st floor of the multi-purpose Vits building 100 m south of Toyotashi station, open until 2am) is the only Western pub in town, and as such usually well-frequented by locals and Toyota expats from all over the world.