visiting the great wall of china

Yes, flying into Beijing and hooking up with a local day tour provider for a trip out to one of the access points on The Wall is how to do it. Fact is - it's the only way to do it since independent travel around the country is severely restricted. The trip will feature a guided tour via motor coach or van (whichever you choose) out to the wall, but will also include stops along the way for "shopping opportunities" ... everything from silk factories to cloisonne manufacturers to herbal medicine shops depending on who your guide may be related to. There's no getting around it unfortunately.
Know that getting a visa for mainland China can be an expensive and time-consuming affair so you'll need to add the process of getting one into your planning. The State Dept. website can walk you thru the process.
You can get a same-day Chinese visa at the airport in Hong Kong - it's not cheap but they do offer quick service ... about a 6 hour turn-around time as I recall. You can take the train from the airport into the city for a little sightseeing while you're waiting and then continue on to Beijing.
Might add that there's a lot more to see in Beijing (and China) than the Great Wall. Having jumped thru all the hoops required to get a visa you really ought to make it worthwhile by extending your time in the country.
I'd also add that the air pollution in and around Beijing is probably among the worst on earth - there are seasons of the year when you can barely see across the street because of smog or blowing sand. October seemed to be the best time of year to visit. Once the first cold fronts of Autumn blow thru everything cleared up nicely.

It is a 6-hour flight from Singapore to Beijing, 4.5-hour from Bangkok, so it is not ideal.
Plus, there is much, much more to Beijing than the Great Wall: Forbidden City, Temple of Heaven, Lama Temple, Summer Palace... I would say Beijing deserves 4 full days, 3 for a quick visit. Any less feels like shortchanging the destination. And given the distances involved, it really does not combine well with SE Asia.

Agree with balso, do China when you can see more.

Yes, I have been to China three times and the Chinese Visa is a pain and expensive. You need to hire a visa acquisition company.

Tom_MN, a couple of notes above: regarding your comment about Thailand being like Death Valley in the summer, I get the general drift of your message, but I've been to Death Valley a couple of times, and it's at least very dry, which I can handle. But according to most of what I've read (for I've never been there), Thailand, or most of it anyway, is not only hot but humid, which for me would be devastating. I'm wondering whether Thailand in the spring or summer is literally like like Death Valley in being hot but dry, or just in being hot? I ask only because my willingness to visit a place (or not) often hinges on factors like this. (And I realize the humidity may vary with location within the country.)

I have been to Thailand in the Summer, it was hot and humid. I managed just fine, but I am from south Georgia where it is also hot and humid in the Summer.

I visited Singapore and Malaysia in late March, since those countries are practically on the Ecuador, whatever season you visit, it was hot, but not so bad for me.

I visited Indonesia in in March/April and had the same experience. The Philippines in the Summer was actually not bad, but there was always a nice breeze.

We did China late Summer, early Fall and it wan't really hot until we were in the southern part of the country.

I have been to three different locations of the Great Wall as well as where it ends. It was good to see them but there are many other places and sites in China that are far more interesting to see. But that was back when it was easy to travel to China, get a visa in advance. I would wait until things with China improve. I went there three times, to different regions.

Considering the flight times, this would be like taking a vacation in California and then deciding to see the Statue of Liberty in NY for a day!

I have been to China six times and there’s so much to see there! It’s big and it’s fascinating. I barely scratched the surface in Beijing. (And the others are right. Chinese visas are not easy to get and expensive too). Save the Great Wall for a proper trip to China.

I’ve been to both Thailand and Singapore as well. There’s more than enough in those places to fill your time. It is humid in both locations, so plan for some downtime in some air conditioned space too!

I want to thank those who addressed my Thailand/humidity question, above. It seems that my suspicions were correct, at least for Bangkok.

TravelChinaGuide

We took the bus when we were there. It's the cheapest and fastest way to get to the Great Wall, if you don't mind Chinese people asking you questions and taking photographs with you :). You could also take a tour but you'll pay a lot more to see the same thing. The advantage of the bus is also that it's a direct route that doesn't stop at tourist shops. Nor do they try to sell you stuff.

Yes, I have been to at least three locations along the Great Wall. One was at the far western end.
You can enter China for a very limited time without getting a Visa as a transiting passenger with proof on onward travel. . If you have the chance, do it!