I was going to suggest those very ones (except Moonraker). Does that mean I have the mentality of a 10 year old boy? 
Still, though, I have to agree with Krokodil that Bond is a pretty dubious role model, mostly for how he treats women. But then again, I know plenty of sensitive, decent men who watched Bond films as youngsters and they didn’t do them any apparent harm I suppose…
There is only one Bond film worth watching. Anything that came after this one has serious continuity issues.
Underwater Esprit was For Your Eyes Only
A few more reasons for choosing For Your Eyes Only*:
Carole Bouquet’s character is an independent, strong-willed, murderous Bond girl in her own right. She and Bond meet when she’s shooting the bad guys with her crossbow, saving Bond in the process when he’s on the run from those henchmen. (His big getaway moment is when he jumps from a wall using a table canopy umbrella as a parachute – one of those stupid stunts the little kid in me always wanted to try.) Plus crossbows are always cool.
The ski jump/ski chase scene, with the evil Aryan East German Commie Olympian chasing Bond with a machine gun. Ski jumps and ski chases are always cool.
Bond & allies taking the bad guys’ stronghold on a high monolithic promontory, which requires some tricky mountain climbing. Terrific location shooting, in both senses of that term (the site was IRL a Greek Orthodox monastery).
Nope, it was Spy Who Loved Me (remember Barbara Bach’s “Agent XXX” saying she’d stolen the plans for that car, and Moore dropping the fish out the window on the beach, and the silly reaction shot of the guy with his bottle of wine?) There was lots of scuba diving in For Your Eyes Only, however.
Another vote for You only live twice,still the best bond movie IMO.
You Only Live Twice is possibly the most juvenile of the Bond films, and thus best for a 10 year old. From Russia With Love? For Your Eyes Only? On Her Majesty’s Secret Service? Come on, guys, these are films that approach reality (albeit, starting from a very far distance). You might as well sit the kid down and make him watch Tinker, Tailor, Soldier, Spy all the way through. You Only Lives Twice is perfect for a ten year old (I actually saw it at seven or eight) because of everything lieu lists, and because it is when the Connery Bond films stopped taking themselves remotely seriously.
I’d follow it up with Diamonds Are Forever (even sillier, especially Bambi and Thumper), some of the later Roger Moore films (The Spy Who Loved Me, A View To A Kill), and any of the utterly silly Pierce Brosnan films except for Die Another Day, which was too silly for anyone who has graduated from Spongebob Squarepants. Once he’s started into reading the classics, fill him on on From Russia With Love, Thunderball, On Her Majesty’s Secret Service, The Living Daylights, and finally Casino Royale. Just as grown men don’t drink mother’s milk, children should not drink fine whiskey.
Oh, and Goldfinger? Not just silly, but actually absurd. If you pay attention to the plot, you realize that Bond does not one thing right after the opening scene. All he does it get himself repeatedly captured, tortured, imprisoned, and nearly executed, and gets both Masterson sisters killed too boot. Notice that fancy tricked out Aston Martin he drives? Q Branch might have well issued him a Lada for all the good it did him, and it was only blind luck that Auric Goldfinger’s blithe indifference to the absurdity of his own program, plus his lack of awareness that Ms. Galore’s interests lay elsewhere, which doomed his plan to failure. The real hero of the story is Pussy Galore, if for no other reason than to get those two words together to pass a network censor.
Stranger
I’ll cast my vote for Octopussy. It was my first Bond, it’s the one that hooked me, and (sentimentality aside) I think it was the most fun Bond, especially for a young kid. Some of the highlights:
[ul]
[li]The opening chase, with the mini-plane that had fit into the horse trailer[/li][li]Bond beating Kamal Khan at backgammon by using the villain’s loaded dice[/li][li]The “Most Dangerous Game” jungle chase, complete with Tarzan act[/li][li]The chase through Delhi, where he uses a lot of stereotypical Indian props to fight off the villains[/li][li]Also amusing during that chase was when he threw money to the crowd behind him, causing them to block his pursuers[/li][li]The circus train fight, and the circus scene itself[/li][li]Probably the most eye candy of any Bond film[/li][/ul]
It’s not the most “robust” of Bond films (i.e., the most satisfying for an adult), but it’s great for hooking a kid on the series.
After he has seen whatever Bond movie you choose, I suggest you encourage him to read a Bond novel (as I’m sure you will). That way, he can be Bond, and not just watch him. He can drive an Aston Martin through the streets of Paris and face down a villain at baccarat in Monte Carlo!
On the other hand, he can be a chain-smoking alcoholic bastard. I think Book Bond might suffer from the same problems as does Casino Royale for a 10 year old. 
I think it’d probably go with For Your Eyes only, and either of the first two Brosnan films.
As long as it’s not The Spy Who Loved Me. One of the chapters of that book begins, “All women love rape.” And that’s where Fleming lost me as a reader (well, I finished the book, and thought it was crapulent, so didn’t read any others) and as an idea, not appropriate for a 10 year old.
When I was little, “I loved View to a Kill.” I know, I know, a very bad one, but I seem to remember sharks and I was very big on sharks at the time.
Fleming thought about the same as you about the book, and sold the film rights to the novel on the explicit basis that only the title was to be used. There is nothing in the film that in any way, shape, or form resembles the movie. You also have to bear in mind that the novel was told from the viewpoint of a very screwed up woman narrator, and is not the voice of the author or Bond. One wonders what you would make of the novels of Patricia Highsmith.
Stranger
That was the first one I saw in the theater; just turned 11 when it came out. Not sure if it was my first ever, though.