I am living in Phuket and my Thai wife and I own a house here.

I will shortly be applying for a marriage visa. Do I need to apply at Immigration here in Phuket or can I apply in Bangkok?

No "marriage visas" as such, exist.

It would help if you were to tell us on what basis you are currently staying in Thailand.

Visa's are obtained out of the country, Extension of stay based on marriage are obtain in the country, go to your local immigration if you require an extension.

There is no marriage visa.

What kind of entry do you have now?

If you have a non immigrant visa entry you can apply for an extension of stay based upon marriage at Phuket immigration.

If not you would have to go to Bangkok to do a conversion to a non immigrant visa entry. This would require two trips to Bangkok because they will do a 15 day under consideration stamp when you apply. I suggest a trip to Penang for a single entry non-o visa.