Like others have said, it depends on the character and the setting. A character from the United States would likely use Imperial units unless they are in a few career tracks.
Scientists will always use metric units as they are better for more precision (the difference between 32 and 212 is rather arbitrary... 0 to 100 is an easier concept to grasp). Also, science is more international and thus, Imperial units are in a minority of actual scientists.
People in the U.S. Military will typically give distances in Kilometers (called Klicks) and meters when over the radio. This is because since WWI, the U.S. has always fought with foriegn allies on their side. Additionally, it's the unit most likely to be given by a questioned POW which may prove crucial for immediate intelligence. Knots will only be used for speed over water (and in Aviation).
One easy work around is to never give distance in kilometers or feet, but rather in length of time it will take to get there. This is called "Plot Speed" as your position from your destination is in relative to your plot. A three day trip is going to be three days to everyone, no matter which distance measurement you use. If it is from a real world place to a real world place, (New York to L.A.) you can use google maps to find the length of time it will take to traverse the distance in the mode of transit you prefer. Keep in mind that this assumes no down time (resting your feet, getting gas, delays along the route). From NYC to LA, it's 5 hours, 50 minutes by Plane, 2 days and 13-18 hours by public ground transit, and 41 hours by car, and 921 hours (better part of 38 days) by foot.
If you need to give a height, it's better to translate for your audience, though a meter is about a yard in US measurements (A yard is 3 feet and a Meter is 3 feet 3 inches and some change... it's a good guesstimate, but keep in mind the difference between one yard and one meter is better than 2 yards vs. 2 meters (6'0" vs. 6'7" (rounded to nearest inch).
The U.S. does have some familiarity with Liters as both Pepsi and Coca-Cola use 2 liter bottles for their large bottle products. It's not uncommon to see a liter bottle for sale, though typically Americans will buy small soda in 12 oz cans (354 ml), 20 oz bottles (591 ml). All other beverages such as milk and juices are sold in gallon jugs, with quarts, the next step down, being slightly smaller than a liter (1 quart = 0.94 l). Liquid in the U.S. is probably the easiest to dirty convert as 1 quart ~= 1 liter and 4 quarts = 1 gallon, so you just need to take your number, divide it by 4 and you got your gallon value that is close enough. This isn't as easy in the UK as the British Gallon is 1.20 to the U.S. Gallon, but with an amount that big no one really cares. The Pint is usually used in the U.S. to sell small single serving milk cartons, and is 4 pints to a Quart. Again, don't worry too much about this as the Liter is used by Americans and they will get the general concept.
Weight is in Pounds and Ounces, though Ounces are rarely used unless it's just that light. They don't line up with Kilograms or Grams well, and really, they are not the same measurements. For example, you would weigh less in Pounds on the moon than on Earth, but you would have the same weight in Kilograms on either body. The closest Imperial unit for the Kilogram is a Slug, but don't expect anyone who uses Imperial Weights to use it. A Pound is Mass X Gravity. This makes the conversion between the two units difficult to grasp and it's further complicated that the British do also use the Stone, which Americans have no concept of.
In dialog, the American will almost always rely on Imperial measurements unless noted otherwise in the above. Canadians, to my knowledge, are largely the same way. The English are able to convert better, owing to being one English Channel away from Metric users. Aussies will use both, but they lack any concept of an insane travel distance (600 miles to an event is not viewed as a long distance as it would be in Europe or even the U.S. This has more to do with Australia having a lack of major population centers that is not seen in Europe or the U.S.). Kiwis are comfortable with both.