Klimt was part of the Vienna Secession, you could look for some of the other artists in that group.
Painters that you might like are;
Alphonse Mucha
Gustave Moreau
Tamara de Lempicka
Egon Schiele (influenced by Klimt but different)
Ron Kitaj (not all of his, but some may appeal)
Hundertwasser(patterns and spirals)
If I think of any more I'll add them later.