*Jumps up and down like a maniac*
Yeah, you said no parakeets, but I think they're the best choice. If you give a lot of time and make sure they know you love them, they could become "cuddly". And if you aren't willing to wait a long time for the bond between bird and owner to form, then you really should not be getting a bird- or any pet, for that matter. No pet is treated as well as it can be treated if there's impatience involved. Oh, and 'keets do best in pairs. That still probably won't make a large price difference, you can get good parakeets for small prices. And if you need any help with them, just PM me. Dawn has done her research.
And might I suggest a Diamond Dove? At my local PetSmart, you can buy them for around thirty dollars a piece. They don't need toys or anything. But I think they do best in pairs. And they are really beautiful animals.
I do NOT suggest finches if you want "cuddly" birds. Finches are loud, jumpy and fast. And if one of them gets out the cage, you can just kiss it good bye if you have an open door or window. It would be the same with other birds, BUT most small birds cannot fly as fast as the finch. And if you have a limited budget, cockatiels are probably not the way to go, either. Compared to many birds, such as the conure, their prices may not seem high, but they are still very expensive, considering all of the things they need.
If you need any help or a few more recomendations, just PM me. I am a to-be parakeet owner, and I've done lots of research on them, and quite a few other birds as well.