This subject is involved and complicated but there are a few guidelines I have discovered after some research. This is my interpretation, and is totally open for review. I have posted links in the text where I have gathered information as well as other relevant links.
Range versus speed.
If your doing a flight that is the maxium range of the aircraft your flying, you will need to climb to a high altitude around the ceiling hight. This will ensure fuel efficency. You will go slower and your flight will take longer but you will use less fuel as there is less resistance. Ensuring you will make your destination and complete your flight without running out of fuel.
But If your flight is short and well within range, you may wish to go as fast as possible, so you want to find an altitude where you get speed, somewhere between 29,000ft and 34,000ft, ( rough estimate ).This also depends on the wind currents and jet streams and the direction your travelling (see below on jet streams).
This is a copy of a forum posted on this subject and is the reply to the question asked.
For just about any aircraft, maximum fuel efficiency is typically obtained at the service ceiling. The higher the aircraft, the thinner the air, and the lower the drag, allowing a greater distance to be covered for a given fuel burn. Engines generally produce less power as altitude increases, but the air resistance decreases faster than the power output, so that overall efficiency is higher. If you want minimal flight time, though, the picture changes, and you can't have minimal flight time and minimal fuel burn at the same time. For a small, normally-aspirated aircraft, the service ceiling (where the greatest fuel efficiency may be obtained) might be at 14,000 feet, but the highest true airspeed obtainable might be at 5000-6000 feet. This latter peak in airspeed tends to be close to the altitude at which fuel burn also rises to a peak, so inevitably you have to decide which is more important, fuel burn or speed, and then select a compromise between the two that suits your purposes. There normally isn't any best point to select, because it depends on your priorities. However, if you want absolute minimum fuel burn irrespective of speed, or absolute maximum speed irrespective of fuel burn, there are usually specific points at which you can fly to achieve either of these goals (but not both). Manufacturers provide performance charges that make it easy to find maximum speed or minimum fuel burn. In other cases, you can use the charts to find a compromise that suits you.
This is where it gets complicated. Jet streams are like rivers in the sky and usally travel from WEST to EAST around the globe. The same as world wide wind currents. follow the links below for more detail.
So to get maximum speed you need to travel downwind of the jet stream. or wind currents.
If your direction of travel is against the jet stream or wind currents, you need to try and find a altitude where the jet stream is at its weakest. According to the links above the jet streams and currents are at around 32000ft and above. which means an altitude below 32000ft would be best , but remember this altitude would reduce your range.
It may take a bit of experimenting during flight to find the best altitude. I am sure pilots have this information and the resorces to access that information. however I am not a pilot, but I have found some links that will help you to understand and find these jet streams.
Follow this link to look at current jet streams and there altitudes. click on the part of the world you are flying in. This will bring up another map of jet streams which are coloured green, with altitude and speed range, these are concentrated jet streams. If you can track one of these it will expidite your journey.
This link shows the high altitude wind currents in the northern and southern hemispheres in there broad form. you need to select north or south maps. also you can select animation. and see how they move. The altitudes are generally at and above 32000ft. Blue lines are the winds, the longer the line, the faster the wind. The Black parts are the Jet Streams when you see a (H) this marks the speed within the stream. You can see within the black parts there is gray to white colouring, this is where the strongest currents are. You can see that there are wind currents all over the world, and that they generally move from West to East.
If you are flying downwind of a jet stream and at the altitude that it is at its strongest, it is possible to go extreamly fast, have a look at this forum for information.