That's a decent price for July. Practice ITA fare search. Try to sort out a few basic decisions:

For example, if you are already in Beijing, wouldn't you prefer to fly from there? How much extra would you be willing to pay for this convenience?

Or, is your travel from Beijing to a "far east" city free of cost and you'd rather undertake it even to save small amount?

Do you really wish to drive from West Coast to East Coast, or are you just assuming that it would be chepaer to fly to West Coast (probably so, but renting a car is also expensive)? If you found a great fare to NYC or Chicago, would that be attractive?

At ITA, use the syntax city1;city2;city3 to indicate you can fly from/to any of those cities. Change the "sale city" to LON if you want to see prices in GBP; for USD, leave it as BOS, the default setting.

A few sample fares (one-way, 1 adult+ two children) from a casual check, mostly Air Canada:
Beijing-Vancouver £ 1227
Beijing-Seattle/SFO/LAX £1287
Seoul-Vancouver £846 (July 6 only, £945 on July 7,8)
Seoul-Seattle,SFO,LAX £1098 (July7, a little more other days)

Available fares change all the time. Allow yourself some time to understand what is possible, but then if you see a great fare, book it. However, whether flying from Beijing, Seoul or HKG, be sure to allow enough time to get there and catch your flight. Tickets are highly restricted and any change will be very expensive.

Any questions or doubts, feel free to ask. Here or by pm. Good luck.