Each palace in Seoul has something special. The architecture is generally the same, with similar styles of painting to go with it. A ruler certainly wouldn't get homesick while staying in a different palace! But finding the little (or big) differences that makes each palace special is part of the fun.
English tours of the palace (60 minutes) are at 10:30 and 14:30, though you can wander the grounds on your own. Huwon tours in English (90 minutes) are at 11:30, 13:30, and 15:30. This may change; be sure to check Changdeokgung's website (English) before your visit.
Admission to the palace is 3000 won ($3), with an additional 5000 won charge for the garden; I think it's certainly worth the added fee. Keep in mind that a combination ticket to all four palaces and Jongmyo Shrine is 10,000 won ($10) and includes Huwon (the secret garden). I'm not sure how it works, so ask for details, though it should be good for a full month from the date of purchase.
From Anguk Station (Subway Line 3) take exit 3 and walk straight for five minutes. Or from Jongno3(sam)-ga Station (Subway Lines 1, 3, or 5) take exit 6 and walk straight on Donhwamun-ro for ten minutes.