I've had my parakeet Spike for about a month now and he's hand tame, I can get him to perch on my finger and sit on my shoulder. However, he hates leaving his cage and always scrambles across my hand to get back in. I feed him millet for my hand, I talk to him, so what's up? Also, parakeets are supposed to be curious, active and clownlike, but Spike just sits on his perch and does nothing. I know he's healthy because I took him to the vet not long ago, so what gives?
Since no one has answered you, I'll give it a try. I have two parakeets and I know what you mean by the fact that they aren't very curious. My birds are very wary of everything, anyway, does he have toys like bells? My male parakeet loves his bells and he goes crazy for his mirror. Maybe you should buy him some toys and a mirror, but if he really likes the mirror don't leave it in the cage. My bird wouldn't eat because he wouldn't leave his mirror.
Here's another thought, if your bird is a female than she is going to be more quiet and won't play with toys. This is how my female is, she tweets here and there but won't go near any toy at all. Telling whether your parakeet is male or female is kinda hard. Mostly it's the personality and not the cere that you can tell it from. Your bird sounds like it may be female and that's just the way some female parakeets are.
He may just need a little more time, some do take longer than others to adjust, some can take over a month. A new bird finds comfort in their cage when they're in unfarmiliar territory.
You might also want to think about where the cage is. Something around it could be making the budgie nervous so he just wants to go back to the cage & not be out of it.