I seem to recall reading that dragons were very clever in various places throughout the Silmarillion and the Hobbit. But, at least in the Hobbit, Smaug doesn't appear to be much smarter than your average human:
Is there any evidence that Tolkien's dragons were clever/cunning/smart/tool-users?
Most of the dragons in Tolkien seem quite bestial, but there is one who is described as being very clever and cunning, and in fact makes Smaug look about as threatening as a plastic dinosaur.
Meet Glaurung, father of dragons
He's best described in the material relating to Turin Turambar, so the best sources for him are The Silmarillion and The Children of Hurin.
Evil have been all thy ways, son of Hurin. Thankless fosterling, outlaw, slayer of thy friend, thief of love, usurper of Nargothrond, captain foolhardy, and deserter of thy kin. As thralls thy mother and thy sister live in Dor-lomin, in misery and want. Thou art arrayed as a prince, but they go in rags; and for thee they yearn, but thou carest not for that. Glad may thy father be to learn that he hath such a son; as learn he shall.
Glaurung is pure malice and entirely lacking in Smaug's susceptibility to flattery; he has wide knowledge of events in Middle-earth, seems to possess some mind-reading ability, has a hypnotic voice to rival Saruman, and is capable of placing people under enchantments so powerful that they totally forget their entire past. He overthrows an entire ancient High Elf kingdom and sets in motion the events that lead to the ruin of a family of First Age heroes. Balrogs follow this guy into battle - one mean and vicious worm, indeed.
Smaug showed his weaknesses to Bilbo not immediately, but after Bilbo appealed to his pride:
"I might have guessed it," said Bilbo. "Truly there can nowhere be found the equal of Lord Smaug the Impenetrable. What magnificence to possess a waistcoat of fine diamonds!"
"Yes, it is rare and wonderful, indeed," said Smaug absurdly pleased. ... The dragon rolled over. "Look!" he said. "What do you say to that?"
"Dazzlingly marvelous! Perfect! Flawless! Staggering!" exclaimed Bilbo aloud ...
Smaug's greatest weakness is his ego. He doesn't trust Bilbo at all, and exerts the full force of his personality to draw Bilbo out (physically and psychologically) and to overwhelm him by thoughts of how useless his task is, and how he's likely being fooled by the dwarves:
"Well, that's just like them. And I suppose they are skulking outside, and your job is to do all the dangerous work and get what you can when I'm not looking-for them? And you will get a fair share? Don't you believe it! If you get off alive, you will be lucky. ... even if you could steal the gold bit by bit-a matter of a hundred years or so – you could not get it very far? Not much use on the mountain-side? Not much use in the forest? Bless me! Had you never thought of the catch? A fourteenth share, I suppose, Or something like it, those were the terms, eh? But what about delivery? What about cartage? What about armed guards and tolls?"
Now a nasty suspicion began to grow in [Bilbo's] mind—had the dwarves forgotten this important point too, or were they laughing in their sleeves at him all the time? That is the effect that dragon-talk has on the inexperienced. Bilbo of course ought to have been on his guard; but Smaug had rather an overwhelming personality.
But when Bilbo spends some time stroking his ego, Smaug reacts as Bilbo hoped. This is not lack of intelligence, but simple possession of a major weakness that Bilbo is quick to exploit.
Smaug leaves his lair twice in the story: once (after Bilbo steals the cup) to try and scout out Bilbo, at which he fails; and once after the conversation between the two to try and destroy Bilbo and the town that (as Smaug believes) sent him to steal the treasure. In both cases, of course he knows Bilbo is still in the vicinity; his objective is to find and then destroy him.
In addition, what can Bilbo do? Smaug knows how immense his treasure is, and how extraordinarily unlikely Bilbo is to be able to steal any significant portion of it; and he doesn't see any particular reason to believe that Bilbo or anyone else could seriously hurt him:
"Revenge!" he snorted, and the light of his eyes lit the hall from floor to ceiling like scarlet lightning. "Revenge! The King under the Mountain is dead and where are his kin that dare seek revenge? Girion Lord of Dale is dead, and I have eaten his people like a wolf among sheep, and where are his sons ) sons that dare approach me? I kill where I wish and none dare resist. I laid low the warriors of old and their like is not in the world today. Then I was but young and tender. Now I am old and strong, strong, strong, Thief in the Shadows!" he gloated. "My armor is like tenfold shields, my teeth are swords, my claws spears, the shock of my tall a thunderbolt, my wings a hurricane, and my breath death!"
Why would he worry about Bilbo? He could hunt him down at his leisure.
As far as tool use: Why should that be a mark of intelligence? Clearly Smaug wouldn't have been able to make a tool; his claws were unsuited for it. But being able to think, plan, and deduce from evidence are clear signs of intelligence which Smaug exemplifies well.
Smaug certainly had his flaws, in that he was selfish, prideful, and easily flattered; but I see no reason to believe that he's not extremely intelligent.
