Bellevue is a lovely town just east of Seattle. They are separated by Lake Washington. It's a great town, and the entire east side is a great place to live.
The school districts on the east side are all good. Bellevue School district regularly gets one of their high schools in the top rankings in the country. Mercer Island School district, Northshore School district, and Redmond SD and Issaquah SD are all good ones too.
Overall, you'll find just about any of the neighborhoods on the east side to be safe. "Diversity" here means lots of Asian & Indian families more than hispanic or African American. And while this tends to be a "less diverse" place according to the census (80% caucasion or something like that), this is a liberal, accepting place to live in just about any neighborhood.
One issue for you may be the cost of living. You haven't said where exactly you are coming from. Mercer Island, Bellevue, Issaquah and Redmond all have great homes, but they can come at great prices. Start looking at the multiple listing service now to see what your money buys. I like the real estate web site of Windermere - www.windermere.com that will show all listings in the MLS.
If after looking you feel like you need to aim for a neighborhood with lower real estate values, some of the places to be looking include Bothell (to the North), North Bend (to the east in the foothills), and Renton (to the south). The further out you go (north, south and east) the more reasonable the prices will be.
Keep in mind that traffic isn't great here. It can be an hour commute from Bothell to downtown Bellevue during rush hour. One of the two bridges that cross Lake Washington is a toll bridge that makes traffic better, but at a cost to you to get into/out of Seattle.
Good Luck!