By far, the actual cheapest spend to earn miles to keep the account active: buy a song on iTunes through the MP mall. You get 2 miles per dollar spent. All you have to do is go to mileageplusmall.com, and choose iTunes as the store. Click on the "go shopping" link once there, type in your MP number, click go, and iTunes will open on your computer. When you make the purchase, the miles will credit to your account. Or, find another retailer that has something you were going to buy anyway, and buy it through the mall.

One caveat: the miles may or may not credit by 7/31. I can't remember how long it took mine to credit.