General respect and appreciation:
* Respect
* Esteem
* Applaud
* Praise
* Honor
* Revere
Emphasis on beauty or excellence:
* Appreciate
* Marvel at
* Be impressed by
* Be in awe of
* Be captivated by
Emphasis on liking or fondness:
* Like
* Love
* Cherish
* Be fond of
* Be drawn to
More informal synonyms:
* Think highly of
* Look up to
* Be a fan of
The best synonym for "admire" depends on the context of the sentence and the specific feeling you want to express.