Award space is wide open in Business Class on United flights to Brussels and Amsterdam for Summer 2017 for 2+ people. That means you can book your family flat beds to Europe for as little as 40,000 miles plus taxes with no fuel surcharges.
Product
United Business Class features a comfortable flat bed, but it isn't up to the standards of the absolute best products in the world because there are as many as eight narrow beds per row.

Only true aficionados will complain.

United is running two award sales at the moment:

20% off domestic awards
Up to 25% off awards to Asia (announced here-- note that the promo code doesn't activate until August 11)

20% Off Domestic Awards
Here are (what look to be) the conditions for the unannounced domestic sale.

Register here
Economy Saver only
Roundtrip only (open jaw itineraries within the same region also count)
Must book by 11:59 p.m.

I just booked myself a $1,233 economy flight from Hawaii to Chicago for 17,500 Singapore miles and $5.

You probably already have the miles I used, so you're only a 10 minute phone call away from a trip to Hawaii that costs thousands of miles fewer than it "should."

The basic idea is that you don't want to use United, American Airlines, or Delta miles to fly to Hawaii. You want to use their planes, but you want to book those flights with miles issued by foreign airlines, which for whatever reason, offer far cheaper award prices to

Although United offers no stopovers on one way awards, the airline allows one stopover on roundtrip awards in addition to your destination. This can lead to all sorts of outsized value:

You can see 2-3 cities for the price of one on your next trip.
You can book a later Free One Way from your home airport to somewhere else in the United States or Canada after you next roundtrip for no extra miles.
You can book three related or unrelated one way awards together and save miles.

I get questions all the time like this:
Hi, I have a million American Express Membership Rewards/Chase Ultimate Rewards/Citi ThankYou Points, what is the best transfer partner to go from [here] to [there.]
There are basically two ways to answer the question:

Look at award charts of all the points' transfer partners and then look for award space using the cheapest miles. I used this method to suggest to my friend that he transfer his Membership Rewards to Flying Blue miles to get from Denver to Tel Aviv.

Through Friday (May 27, 2016) at 11:59 CT, United is offering a 100% bonus on purchased miles. The size of the bonus depends on the number of miles you buy, with the largest 100% bonus kicking in at 40,000 miles purchased.

United miles normally cost 3.5 cents per mile plus a 7.5% tax, bringing the full price to 3.76 cents each.

Download a free app and get 1,000 free United miles in a few weeks.

There are three steps:

Register for the promotion here. (The promotion is that if you download a personal finance app called Prosper Daily and register your account, you get 1,000 free United miles.

I know most people just want to go somewhere and come back with their miles, but I am biased toward BIG trips. For the most part, the best way to book such big trips is as a series of one way awards with many different types of miles, taking advantage of the sweet spots with each program.

All Nippon Airways (ANA) has reduced fuel surcharges drastically on awards that travel to or from Japan. Now you can fly to Tokyo from the United States for 75,000 miles in flat bed Business Class roundtrip plus low taxes plus a $4--yes four dollar--fuel surcharge. That's tens of thousands of miles fewer than competitors charge.

The above screenshot is of a roundtrip Business Class award flying ANA between Los Angeles and Tokyo in February 2017.
Routing Rules
ANA has two award charts.