Mount Saint Helens / Mount Rainier tour:

There aren't many useful navaids around so this is pretty much VFR. Check your gyroscopic compass and make sure it matches your magnetic compass. Set the heading bug to 60.

Depart from Kelso Longview / Southwest Washington Regional Airport (KKLS) at heading 60 magnetic and climb to around 7000 feet. You've got some time, so you can take it nice and easy. 300-500 fpm should be plenty. This is more of a "cruise climb." Plenty of time to set your autopilot to heading mode, lock in your vertical speed, and adjust your throttle and mixture for optimal performance. Also to adjust cabin heat for comfort.

After 10-15 minutes, you'll encounter Mount Saint Helens (you can't miss it). Feel free to circle around a few times if you like. The best views are from the north and north-east. While you have the plane under manual control and you're having fun, this is a good time to adjust your heading bug to 0 (due north). When you're satisfied, you can depart from Mount Saint Helens heading north. Climb to around 12,000 ft. if you can. This is subjective and depends on how close to the summit you want to get. Aside from the mountain itself, there are no obstacles this high. Again, you've got time (15-20 minutes), so you can take it nice and easy. Don't bleed off too much airspeed in favor of elevation. It is a challenge to get most single-prop planes to this altitude, even if with the perfect fuel mixture and carb heat. This is a perfect chance to try it though. If you want to try this on hard mode, FlightGear simulates windshield, wing, and carburetor icing conditions too :)

Eventually you'll come across Mount Rainier (you also can't miss it). Ranger Creek Airfield (21W) is buried at 2600ft in the valleys on the eastern side of the mountain. It's pretty challenging to locate/land at. If you want to circle the mountain I recommend going counterclockwise to locate the field from altitude on the first pass and help line up a lower altitude approach from the south on the second pass. The terrain map on the G1000 can be very useful here, allowing you to "see around the bend" of the valley you're flying through.

Total flight time is about 45 minutes - 1 hour in a Cessna 172 Skyhawk.

Flying up to Lukla from Kathmandu:

Lukla (VNLK), also known as Tenzing-Hillary Airport, is one of the most ridiculous airports ever built. It sits at an elevation of 9300 ft, surrounded on all sides except the trench you approach from by mountain ridges reaching up around 13,000 feet. It is also incredibly short and has an absurdly steep slope to make landings and take-offs possible. It is the closest airport to Mount Everest's southern basecamp (the Nepal side).

You depart from Kathmandu International Airport (VNKT) in a STOL aircraft (highly recommend the DHC-6 Twin Otter, as seen in the above video.) VNKT has a VOR/DME station at 112.3 MHz. After taking off, follow a heading of 93 from the VOR station. I don't remember exactly how high you need to get, but there will be a couple mountain ridges in your path and you will have to climb to something like 13,000 ft. You don't want to make your final approach from this altitude though. When your DME reads about 70 nautical miles, you have to turn north. By now you should be at about 11,000 ft, and now is the time to start searching for the right crevice to snake your way up until (hopefully) the airport appears on your right. A GPS or Terrain map will be very useful.

Going back is basically the same thing in reverse. It is a lot more simple though, since you can home in on the VOR station from any direction once you're clear of terrain. It is probably a good idea to fly out of Lukla first, before flying in, just to get an idea of what the terrain looks like. That said, you need to take some extra precautions when taking off, such as turning the throttle all the way up while sitting on your breaks as long as you can until they are no longer capable of fighting the engines, then launching. Flaps all the way down (that's 7 or 8 clicks on the DHC-6). You might also need to lean your fuel mixture a bit at that altitude to get the most performance out of your engines, but I don't remember exactly how that works on the DHC-6. It seemed less temperamental than the Cessna about it, but I can't tell if that's how the plane actually works, or how the model was designed in this particular simulator.

Lukla places you only 15 minutes or so (as the crow flies) from Mount Everest, but you need a jet with a pressurized cabin if you want to get anywhere near the summit. These tend to be heavier while STOL (short takeoff and landing) planes need to be light as possible. The STOLs are basically skydiving planes, not airliners. You could take off from Kathmandu in an airliner or fighter jet though, follow a very similar course (leaning maybe 5 degrees more north), and check out Mount Everest itself (and getting there much faster than a prop plane).

The flight is about 35-45 minutes each way.

Disclaimer: I've only flown these in FlightGear and X-Plane myself.

Also, thumb through this free e-book when you get the chance.