Although he didn't have any money, he called a taxi. (Though could also be used here.)
"I will call a taxi. I don't know where to find one, though."
The above example uses though as an alternative to but, placed at the end of the sentence instead of the beginning: "I will call a taxi but I don't know where to find one."
Despite on its own must be followed by a noun, verb participle or gerund:
Despite the rain, he went outside.
Despite going out in the rain, he didn't get wet.
In spite (two words) has much the same meaning and use, but is always followed by of:
In spite of the rain, he went outside.
Hope these examples help.
Student or Learner