Open a United Visa from Chase. Often banner ads that help Flyertalk here, plus links on united.com. Bonus offers vary, but 20000 mile offers almost always, 21000 common, 25000 was around a lot this summer. Don't be skunked by the "17500 free miles" offers in the airports and on the boarding passes; there's always something better than that.

Bonus miles post a couple of days after your first statement cycle from Chase, as do the purchase miles. Common offers usually require a purchase, sometimes $250 in purchases, before the bonus miles post. Most offers waive the first year's fee.

More miles than you need (unless you want to book a higher class of service, or have to use a Standard award instead of Saver for the dates you want), but perhaps the quickest and easiest way, assuming acceptable credit.