What are good conferences for algorithms about finite automata?
The main conferences where automata are among the main topics are ICALP, LICS, STACS, CSL, MFCS, FSTTCS. 

If you feel your paper is not strong enough for these conferences (which accept about a quarter of the papers that are sent each year), you can send to conferences which are a little less exigeant.

The ICALP submission deadline is soon (in a week), after this the next in the list is FSTTCS I believe.

These conferences are all european (except FSTTCS from India), it seems that automata are less popular in USA, but it might be that your results interest some people at STOC or FOCS.