Yes! The Republican State Leadership Committee, an organ of the Republican Party, maintain a handy list of which state offices are controlled by which party. You can find it here:
If you want actual lists of names of state elected officials, the way to find them is by googling the name of the body eg "california state legislature" and finding its official website.
This is perhaps beyond the scope of your question, but if you want to find more info on local/city elected officials, a good place to start though is by reading voter guides in the given states your interested in. They are published every year by each state's elections office and provide nonpartisan information on every office that is up for election, as well as biographies of candidates.
Here's an example of one from Washington State:
Hope this helps.