The order depends a lot on what character one plays, I think. A Dalish or a mage may feel best visiting their own people first. A city elf may want to return to Denerim. A dwarven commoner may want to check on their sister and thumb their nose at the upper crust with the new Grey Warden status. Same with a noble for slightly different reasons, maybe. A human noble, which is what I am playing first, seems to have the fewest "ties" or reasons to go anywhere in particular since, sadly, you can't return to Highever.

I knew about Wynne so I did the Circle Tower first, and the stat bonuses were a sweet surprise so I can definitely recommend doing it as early as possible. After that I did Redcliffe, then went to Denerim to follow the lead on Brother Genitivi, then to the Forest since it was the closest, then to Haven and the Urn. After that I returned to Denerim, then back to kill the high dragon, back to Denerim
again, and hit Orzammar last. I'd taken a peek at the place earlier but decided to return later (my character didn't want to get involved in politics and hoped the dwarves would settle the matter on their own).
Unless you're really keen on getting Oghren early, I think for story reasons and suspense it's best to save Orzammar for last. The Deep Roads, even if they don't
really feel like it due to fast travel and small area maps, would be a truly epic journey even for more experienced travellers. And as touching as the climax of the Forest is, or as intense as the high dragon battle is, I think the Deep Roads have the biggest impact.
Small spoiler space, just in case. I know this is a spoiler forum, but not everyone wants every thread to spoil everything, so ... don't look if you don't want to know about what happens in the Deep Roads.
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You learn about darkspawn procreation in a truly hideous way. You learn about golems. You see the darkspawn army on the march and even see the sodding archdemon itself! I think doing Orzammar first would make all the other subplots feel decidedly ... quaint in comparison. Especially when you and Alistair later have the archdemon dreams and decide yes, it's really a Blight and the archdemon is scary. Er, yes, having seen the thing
in the flesh already, the dreams would be rather superfluous and probably not half as horrible.
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End spoiler space. In summary: Circle Tower first, Orzammar last would be my recommendation.