If I have a military city or a GP city, is it worth it to ever convert the hammers to research, wealth, or culture if I don't have anything to improve the city specialization or should I build some different building like a barracks in a GP city or a temple in a military city?

Military City

If your military city is suffering from the happiness cap, or you're looking at building Cathedrals and need the Temples, then a Temple might not be such a bad idea. I wouldn't see much value in building a Temple if the city can't grow past the happiness cap, isn't under cultural pressure, and you aren't struggling to find Temples for Cathedrals. Even with the University of Sankore and The Spiral Minaret, it would be difficult to justify a Temple build 'just for the heck of it'. A possible exception may be to run Specialist Priests, which are :hammers: bolstered through the Angkor Wat that will require a Temple - again, situation dependant.

The quick answer would be - build more units, and if you have too many units you should probably use them in a war.

Great Person City

This should be food-rich and therefore good for building Workers and Settlers when not in population-growth mode. If you're planning to combine The National Epic and The Globe Theatre, then this can be used for whipping units in times of excess, and as such Barracks would be a good move.

To some extent this would depend upon the envisaged build of the city, the build options available to it, whether or not you're running The Caste System, and other factors such as your victory target, size of empire, relative position to the AI tribes, if you're 10:science: short of researching your next technology next turn, etc.

^ There are a few 'ifs' and 'buts' associated with this broad question that I'd guess other forum members would like to contribute ...

If you have a dedicated military city (or cities), it should only produce military units unless you need a specific building to enhance the city production or give units experience points - like Heroic Epic, etc.

Otherwise my military cities pretty much only have a granery, courthouse, barracks and forge until the endgame. It should also have a nice balance between production tiles, farms and perhaps a few cottages depending on the situation. In a current game my military city has more cottages than farms, but that's with a finacial leader and probably only until my capital will take over the economic burden combined with Bureaucracy.

If you get an overload of units, you might not use them often enough as Cam H mentiones. You can always build modern experienced units and delete obselete ones if not in war and strapped for cash to maintain a large army.

A dedicated GP farm should pretty much maximise food production and build needed wonders and +happiness buildings. The Globe Theater is a nice addition, but keep on mind that you can only have up to 2 national wonders in every city. National Epic and Oxford are also national wonders and would also be wise to place in your GP farm (you can always have two GP farms ;).

In some circumstances you could produce science with your hammers, but usually I choose to produce units with my GP farm when it dosen't need a specific building or wonder. Imo though, your military citiy should never produce science, wealth or culture with its hammers. Build specific science (GP farm?) and wealth (Wall Street etc.) cities instead nomatter if you are playing a CE or SE or hybrid. :)

Usually I go the other way around. Late game my commerce cities and my GP farm convert their hammers to wealth (so I can raise the science slider) and my production cities build wonders and spaceship parts. Usually by the time they do this there are no good improvements left to build, or by the time they build the last improvements the game will be over.

I would never waste a good production city on building wealth - units is a much better investment. And never ever ever in my military cities.