South Pasadena and Monterey Hills are nice areas where you could find properties that fit your search criteria and price range.
Send me your email address to JamieTian@RodeoRE.com or give me a call at (310) 717-1321 and I would be happy to answer any additional questions you might have and send you a list of properties currently on the market in these areas with 3 bedrooms and under $800,000.
Good areas around Pasadena are La Crescenta, Glendale, Montrose, Pasadena, and some of the small areas east of Pasadena. If you have children, my best advice is sticking to a good school district if you plan on your kids attending private school. With up to 800k, you can easily get a very nice home in those areas. I personally love Montrose or La Crescenta with its small town feel, nice homes, and great old town area and weekly farmers market and monthly events in Montrose on Honolulu St. The street is charming with restaurants and many things to do for the family. Its a quick drive over the 210 freeway to Pasadena and excellent blue ribbon schools.
I would love to help you look for a home and I also offer a commission rebate through escrow which can help cover your closing costs. Feel free to contact me anytime, 818-426-1700