I lived in Claremont for a few years and it was a pretty good city to live in. It's between Los Angeles and San Bernadino, plus it has Angeles National Forest directly to the north, so it's in a really good spot.
At first glance, the average cost of a house in Claremont seems really high, but that's really because it is a very desirable city. The job market is strong and geared towards high paying jobs, so the standard of living is high. The crime in Claremont is also a bit lower than the rest of the state so you will feel safer living here too.
The best area in Claremont is the downtown area. I love to read and there are five libraries and even more great cafes to choose from. There's also a lot of little boutique stores you can find a lot of cool and interesting things from. In the summer, it's very fun to walk through the downtown area to feel how lively it is.